Entropic gravity is like the "brazil nut effect" [0] [1]. The idea is that if you shake a glass full of different sized nuts, the large ones will rise to the top.
From what I understand, this is because larger objects have more mass, moving slower when shaked, so as the larger (brazil nuts) don't move as much relative to the smaller ones (peanuts), and because of gravity, there's a cavity left under the brazil nut which gets filled in with peanuts.
For entropic gravity, the idea is that there's a base density of something (particles? sub-atomic particles?) hitting objects in random ways from all directions. When two large massive objects get near each other, their middle region will have lower density thus being attracted to each other from particles hit with less frequency from the lower density region. They sort of cast a "shadow".
I'm no physicist but last time I looked into it there were assumptions about the density of whatever particle was "hitting" larger massive objects and that density was hard to justify. Would love to hear about someone more knowledgeable than myself that can correct or enlighten me.
As an aside, the brazil nut effect is a very real effect. To get the raisins, you shake the raisin bran. To get gifts left from your cat, you shake the kitty litter. It works surprisingly well.
"Many mechanisms for gravitation have been suggested. It is interesting to consider one of these, which many people have thought of from time to time. At first, one is quite excited and happy when he “discovers” it, but he soon finds that it is not correct. It was first discovered about 1750. Suppose there were many particles moving in space at a very high speed in all directions and being only slightly absorbed in going through matter. When they are absorbed, they give an impulse to the earth. However, since there are as many going one way as another, the impulses all balance. But when the sun is nearby, the particles coming toward the earth through the sun are partially absorbed, so fewer of them are coming from the sun than are coming from the other side. Therefore, the earth feels a net impulse toward the sun and it does not take one long to see that it is inversely as the square of the distance—because of the variation of the solid angle that the sun subtends as we vary the distance. What is wrong with that machinery? It involves some new consequences which are not true. This particular idea has the following trouble: the earth, in moving around the sun, would impinge on more particles which are coming from its forward side than from its hind side (when you run in the rain, the rain in your face is stronger than that on the back of your head!). Therefore there would be more impulse given the earth from the front, and the earth would feel a resistance to motion and would be slowing up in its orbit. One can calculate how long it would take for the earth to stop as a result of this resistance, and it would not take long enough for the earth to still be in its orbit, so this mechanism does not work. No machinery has ever been invented that “explains” gravity without also predicting some other phenomenon that does not exist."
It also doesn't account for time dilation in a gravity well however i still think the general idea has some merit if you think of it as being bombarded by massless ‘action potentials’ on all sides with mass absorbing that field to some to enable translation in space time.
I get this is vague spitballing but essentially an ‘action potential’ would allow mass to move. Higher temperature mass interacts more, lower temperature interacts less. Mass with momentum would be biased to absorb more from one side so it travels in a specific direction in space more than others (the idea i’m getting at is that all movement in space only occurs with interaction with this field), this also would counteract issues with moving mass interacting more on a specific side - the very bias of mass with momentum to absorb more on one side means that from that masses point of view it has the same action potentials interacting from all sides. Mass shielded behind mass receives fewer action potentials so experiences exactly the effect that you can call time dilation. Mass shielding other mass from action potentials also means that mass accelerates towards other mass.
Essentially its the above but instead of a massive particle hitting other mass from all sides it’s a field that allows mass to experience a unit of time.
This is a better YouTube video describing granular physics and shows the speed (amplitude) of vibrations can cause counterintuitive arrangements of particles.
At lower speeds you get something akin to Newtonian gravity but at higher velocities you get something resembling MOND gravity where galaxies clusters and large voids appear - no dark matter needed.
Thanks for the link, very interesting. I'll have to check out the paper but just watching the video it seems all these counter intuitive effects can be described from the oscillations being related to the size of the chamber.
For example if I were to roll the chamber at a very low frequency, I would expect the particles to clump on one side, then the other and so on. This is not really so surprising and the frequency will depend on the chamber dimensions.
No, here "entropic" is as in the entropic force that returns a stretched rubber band to its unstretched condition, which (as it tends to be scrunched a bit) is at a higher entropy.
"The stretching of the rubber band is an isobaric expansion (A → B) that increases the energy but reduces the entropy"
[apologies for any reversed signs below, I think I caught them all]
In Verlinde' entropic gravity, there is a gravitational interaction that "unstretches" the connection between a pair of masses. When they are closer together they are at higher entropy than when they are further apart. There is a sort of tension that drags separated objects together. In Carney et al's approach there is a "pressure mediated by a microscopic system which is driven towards extremization of its free energy", which means that when objects are far apart there is a lower entropy condition than when they are closer together, and this entropy arises from a gas with a pressure which is lower when objects are closer together than when objects are further apart. Pressure is just the inverse of tension, so at a high enough level, in both entropic gravity theories, you just have a universal law -- comparable to Newton's -- where objects are driven (whether "pulled" or "pushed") together by an entropic force.
This entropic force is not fundamental - it arises from the statistical behaviour of quantum (or otherwise microscopic) degrees of freedom in a holographic setting (i.e., with more dimensions than 3+1). It's a very string-theory idea.
The approach is very hard to make it work unless the entropic force is strictly radial, and so it's hard to see how General Relativity (in the regime where it has been very well tested) can emerge.
The local theory part of the Carney et al paper (preprint <https://arxiv.org/abs/2502.17575>) is interesting in that it isn't obviously related to string theory / holographic entropic gravity. Instead masses induce a spin polarization near them which is a lower entropy state. Two masses with two polarized spin-clouds will attract each other as the system tries to thermalize to a higher-entropy state. With careful choices of parameters, they can generate any central force, and they explore a particular choice which corresponds to Newtons 1/r^2 mutual attraction.
The paper cannot deal with fast-moving masses at all: it's not just the relativstic regime (where speeds are significant fractions of c) but rather the masses must move more slowly than the thermalization. This is hugely restrictive.
Finally, comparing themselves to the traditional approach of quantizing perturbations (e.g. turning classical (General Relativity) gravitational waves into lots of spin-2 gravitons) the authors write:
The gravitational interactions we observe at accessible
length scales could in principle emerge in many ways from
physics at the Planck scale ρ ∼ mPl/ℓ3 Pl ∼ 10104 J/cm3.
Perhaps the simplest is that gravitational perturbations
are quantized as gravitons, i.e., as another quantum field
theory like the gauge bosons of the other fundamental
forces in nature. This is a perfectly good effective quan-
tum field theory; nothing in principle forces us to aban-
don this picture until energies near the Planck scale.
They also say that while their starting point was being very different from the holographic picture:
we find that the models have a range of free parameters,
and in some parameter regimes become indistinguishable
from standard virtual graviton exchange
Some of this will necessarily by driven by the need to be compatible with General Relativity in the weak field limit. They are not compatible with strong gravity in General Relativity at present.
So while the idea is kinda interesting, I think they are putting the cart before the horse in asking what their model says about things like the interaction between gravitation and entanglement. That's simply unmeasurable by experiment right now whereas the very-well-understood relativistic precession of Mercury's perihelion is completely out of scope for this initial paper.
> From what I understand, this is because larger objects have more mass, moving slower when shaked, so as the larger (brazil nuts) don't move as much relative to the smaller ones (peanuts)
That doesn’t make sense to me. If larger objects move slower, don’t they move faster relative to the (accelerating) reference frame of the container?
Also, conventional wisdom has it that shaking (temporarily) creates empty spaces, and smaller objects ‘need’ smaller such spaces to fall down, and thus are more likely to fall down into such a space.
> That doesn’t make sense to me. If larger objects move slower, don’t they move faster relative to the (accelerating) reference frame of the container?
Yes? But so what? The relevant interaction is between the peanuts and the Brazil it's.
> Also, conventional wisdom has it that shaking (temporarily) creates empty spaces, and smaller objects ‘need’ smaller such spaces to fall down, and thus are more likely to fall down into such a space.
Right, but preferentially under the larger Brazil nuts.
> From what I understand, this is because larger objects have more mass, moving slower when shaked, so as the larger (brazil nuts) don't move as much relative to the smaller ones (peanuts), and because of gravity, there's a cavity left under the brazil nut which gets filled in with peanuts.
I always thought it was because the smaller nuts can fall into smaller spaces, while the larger nuts cannot.
This sounds really dumb, so forgive me. But one thing that's always felt weird to me about gravity is how we consider things to be one body.
Like yes, when we look at earth from incredibly far away, it's a pale blue dot. But all those oceans on it are flowing and separate from the solid ground underneath. Those large boulders on earth that would have their own (tiny) gravitational pull on their own in space are just part of earth's single gravitational force. All the airplanes in the sky are subject to the pull of the earth, but they're also a part of the gravitational pull that pulls other things to earth.
When shaking cereal, the big flakes rise to the top, but tiny bits of dust from each flake also separates and settle at the bottom. But earth, as a whole, has big bits and little bits everywhere all flowing freely. And gravity seemingly treats all those bits as a single object. But with sufficient distance between objects (e.g. different planets), it treats them separately. And with greater distance (e.g. galactic scale), it treats them as one again.
> And gravity seemingly treats all those bits as a single object.
It does not; but when you learned about gravity in school or wherever, you were only presented with scenarios in which it was valid to do so. Specifically, for Newtonian gravity, an object whose density is spherically symmetrical may be treated as a point mass at its center (w/r/t other point masses farther from the center than any point in the first object); this can be seen by integrating Newton's equation.
There's no reason to attribute this to special behavior by gravity with respect to "objects" which you identify. You could decompose a (spherically symmetrical) mass into several different spherically symmetrical "objects" and sum up their influence on a test mass, and the result is the same as if you had treated the original mass as a point mass. The hypothesis that gravity is "treating" the object one way or another now fails to distinguish all these possibilities; it's no longer physically meaningful.
At sufficiently large distances, or for sufficiently large ratio of large to small mass, the difference between, say, a planet and a spherically symmetrical mass is so small with respect to the main effect that it can simply be ignored.
There’s a bit of math you can do where you calculate the gravitational effect of standing on a sphere. You can redistribute the mass within the sphere and it won’t affect the gravitational pull, assuming it’s radially symmetrical.
One of those unintuitive results.
It probably only works in classical gravity but it’s still neat.
My interpretation of entropy is that if you have X states that are equally probable, but not all states are distinct from each other in some sense, then the next state will likely be one where the states satisfying that condition is most numerous.
For example, if you flip N coins, there are 2^N states available once the flip is done. Each outcome has an 1/2^N probability of outcome. There's only one state where all of the states show all heads. While there's only one state where coins numbers 1-N/2 are heads, and N/2-N are tails, so that particular outcome is 1/2^N, if all we care is the macroscopic behavior of "how many heads did we get"--we'll see that we got "roughly" N/2 heads especially as N gets larger.
Entropy is simply saying there's a tendency towards these macroscopically likely groups of states.
Aren't more massive particles smaller though (in terms of de Broglie wavelength, at least), so they'd have a smaller "shadow"? Or do different forces have different cross-sections with different relationships to mass, so a particle's "size" is different for different interactions (and could be proportional to mass for gravity)?
Actually this is currently blowing my mind: does the (usual intro QM) wavefunction only describe the probability amplitude for the position of a particle when using photon interaction to measure, and actually a particle's "position" would be different if we used e.g. interaction with a Z boson to define "position measurement"?
The momentum wavefunction (or more properly, the wavefunction in the momentum basis) completely determines the position wavefunction (wavefunction in the position basis). And we can probe the momentum wavefunction with any particle at all, by setting up identical (say) electrons and seeing the momentum they impart on a variety of test particles. That is to say, the probability distribution of momentum of a particle does not depend on what we use to probe it.
As the position wavefunction is now completely determined in a probe-agnostic matter, it would be hard to justify calling a probe that didn't yield the corresponding probability distribution a “position measurement”.
Entropic gravity is a compelling framework. I think that most Physicists admit that it would be nice to believe that the yet unknown theory of everything is microscopic and quantum mechanical, and that the global and exquisitly weak force of gravity emerges from that theory as a sort of accounting error.
But there are so many potential assumptions baked into these theories that it's hard to believe when they claim, "look, Einstein's field equations."
Jacobson showed that thermodynamics + special relativity = GR. Those are very very general assumptions, so general that it’s hard to even consider what else you might ask for.
I'm not an expert in this field but I think reproducing realistic gravitational interactions seems to require a lot of fiddly set up with heat baths etc.
As an experimental physicist, I refuse to get excited about a new theory until the proponent gets to an observable phenomenon that can fix the question.
This is why I'm skeptical of theories like Wolfram's: It feels like an overfit based on this: It produces all sorts of known theories (special relativity, parts of QM, gravity etc), but doesn't make new testable predictions, or new fundamentals. When I see 10 predictions emerge from the theory, and they all happen to be ones we already known of... Overfit.
But that means we'd prefer whichever theory our species had landed on first. Basing our preference for a theory on that timing seems kind of arbitrary to me. If they're the same in other respects, I'd take a look at both sides to see if there are other compelling reasons to focus on one or the other, such as which is simpler. Of course if they make different predictions that'd be even better, time to get to testing :)
I don't know anything about Wolfram's theory, but one general way to address this is to compare the Akaike information criterion (or similar measures).
The metrics attempt to balance the ability of a model to fit data with the number of parameters required. For equally well-fitting models, they prefer the one with fewer params.
If Wolfram's theory fits as well but has fewer params, it should be preferred. I'm not sure if fewer "concepts" counts, but it's something to consider.
The problem with emergent theories like this is that they _derive_ Newtonian gravity and General Relativity so it’s not clear there’s anything to test. If they are able to predict MOND without the need for an additional MOND field then they become falsifiable only insofar as MOND is.
Deriving existing theories of gravity is an important test of the theory, it's not a problem at all. It's only a problem if you can only do this with more free parameters than the existing theory and/or the generalized theory doesn't make any independent predictions. Seems like in the article the former may be true but not the latter.
Sometimes I wonder, imagine if our physics never allowed for Blackholes to exist. How would we know to stress test our theories? Blackholes are like standard candles in cosmology which allows us to make theoretical progress.
And each new type of candle becomes a source of fine-tuning or revision, progressing us with new ways to find the next candles - cosmological or microscopic.
Which kinda points to the fact that we’re not smart enough to make these steps without “hints”. It’s quite possible that our way of working will lead to a theory of everything in the asymptote, when everything is observed.
we dont know much about black holes, and there are theories which dont allow for proper black holes but do allow for objects that look like black holes in the limit (but e.g. don't produce Hawking radiation)
An observable is always the strongest evidence but there's also the improbability of a mathematical coincidence that can serve as almost as strong evidence. For example the fact that the Bekenstein-Hawking entropy of an Event Horizon comes out to exactly be the surface area divided by plank-length-square units, seems to me almost a proof that nothing really falls into EHs. They only make it to the surface. I'm not saying Holographic Theory is correct, but it's on the right track.
My favorite conjecture is that what happens is things effectively lose a dimension when they reach the EH surface, and become like a "flatlander" (2D) universe, having only two degrees of freedom on the surface. For such a 2D universe their special "orthogonal" dimension they'd experience as "time" is the surface normal vector. Possibly time only moves forward for them when something new "falls in" causing the sphere to expand.
This view of things also implies the Big Bang is wrong, if our universe is a 3D EH. Because if you roll back the clock on an EH back to when it "formed" you don't end up at some distant past singularity; you simply get back to a time where stuff began to clump together from higher dimensions. The universe isn't exploding from a point, it's merely expanding because it itself is a 3D version of what we know as Event Horizons.
Just like a fish can't tell it's in water, we can't tell we're on a 3D EH. But we can see 2D versions of them embedded in our space.
To me, entropy is not a physical thing, but a measure of our imperfect knowledge about a system. We can only measure the bulk properties of matter, so we've made up a number to quantify how imperfect the bulk properties describe the true microscopic state of the system. But if we had the ability to zoom into the microscopic level, entropy would make no sense.
So I don't see how gravity or any other fundamental physical interaction could follow from entropy. It's a made-up thing by humans.
Physical entropy governs real physical processes. Simple example: why ice melts in a warm room. More subtle example: why cords get tangled up over time.
Our measures of entropy can be seen as a way of summarizing, at a macro level, the state of a system such as that warm room containing ice, or a tangle of cables, but the measure is not the same thing as the phenomenon it describes.
Boltzmann's approach to entropy makes the second law pretty intuitive: there are far more ways for a system to be disordered than ordered, so over time it tends towards higher entropy. That’s why ice melts in a warm room.
Entropy isn’t always the driver of physical change, sometimes it’s just a map.
Sometimes that map is highly isomorphic to the physical process, like in gas diffusion or smoke dispersion. In those cases, entropy doesn't just describe what happened, it predicts it. The microstates and the probabilities align tightly with what’s physically unfolding. Entropy is the engine.
But other times, like when ice melts, entropy is a summary, not a cause. The real drivers are bond energies and phase thresholds. Entropy increases, yes, but only because the system overcame physical constraints that entropy alone can’t explain. In this case, entropy is the receipt, not the mechanism.
So the key idea is this: entropy’s usefulness depends on how well it “sees” the real degrees of freedom that matter. When it aligns closely with the substrate, it feels like a law. When it doesn't, it’s more like coarse bookkeeping after the fact.
The second law of thermodynamics is most “real” when entropy is the process. Otherwise, it’s a statistical summary of deeper physical causes.
> there are far more ways for a system to be disordered than ordered
I'm a complete layman when it comes to physics, so forgive me if this is naive — but aren't "ordered" and "disordered" concepts tied to human perception or cognition? It always seemed to me that we call something "ordered" when we can find a pattern in it, and "disordered" when we can't. Different people or cultures might be able to recognize patterns in different states. So while I agree that "there are more ways for a system to be disordered than ordered," I would have thought that's a property of how humans perceive the world, not necessarily a fundamental truth about the universe
I think original post is confused exactly because of “tangled chords” analogies. Something being “messy” in our daily lives can be a bit subjective, so using the same analogies for natural forces may seem a tad counterintuitive actually.
Maybe it would be more fitting to say that it just so happens that our human definition of “messy” aligns with entropy, and not that someone decided what messy atoms look like.
I’d say a bucket of water is more neat than a bucket of ice, macroscopically.
Ice melting is simply the water molecules gaining enough kinetic energy (from collisions with the surrounding air molecules) that they break the bonds that held them in the ice crystal lattice. But at the microscopic level it's still just water molecules acting according to Newton's laws of motion (forgetting about quantum effects of course).
Now, back on the topic of the article: consider a system of 2 particles separated by some distance. Do they experience gravity? Of course they do. They start falling towards the midpoint between them. But where is entropy in this picture? How do you even define entropy for a system of 2 particles?
It has been suggested that time too is derived from entropy. At least the single-directionality of it. That’d make entropy one of the most real phenomena in physics.
But "disordered" and "ordered" states are just what we define them to be: for example, cords are "tangled" only because we would prefer arrangements of cords with less knots, and knots form because someone didn't handle the cords carefully.
Physical processes are "real", but entropy is a figment.
You need some additional assumptions. Only near equilibrium / thermodynamic limit is system linear in entropy. What governs physical processes such as you mention is conservation, dynamics pushing equipartition of energy - but outside that regime these are no longer "theorems".
> Physical entropy governs real physical processes
> the measure is not the same thing as the phenomenon it describes.
There is some tension between those claims.
The latter seems to support the parent comment’s remark questioning whether a “fundamental physical interaction could follow from entropy”.
It seems more appropriate to say that entropy follows from the physical interaction - not to be confused with the measure used to describe it.
One may say that pressure is an entropic force and physical entropy governs the real physical process of gas expanding within a piston.
However, one may also say that it’s the kinetic energy of the gas molecules what governs the physical process - which arguably is a more fundamental and satisfactory explanation.
Bekenstein-Hawking entropy goes up when an Event Horizon increases in radius. That means some mass "falling onto" an EH. So this implies, if our universe is actually a 3D EH, both time and increasing entropy can be explained by one thing: Increasing size of our EH. That is, mass falling onto our EH from outside our universe. It also happens to elegantly replace the Big Bang nonsense theory with something that makes sense. It explains the universe expansion as well. Assuming our universe is a 3D EH makes lots of things make sense that don't otherwise make sense.
Good question. You are absolutely right that entropy is always fundamentally a way to describe are our lack of perfect knowledge of the system [0].
Nevertheless there is a distinct "reality" to entropic forces, in the sense that it is something that can actually be measured in the lab. If you are not convinced then you can look at:
So when viewed in this way entropy is not just a "made-up thing", but an effective way to describe observed phenomena. That makes it useful for effective but not fundamental laws of physics. And indeed the wiki page says that entropic forces are an "emergent phenomenon".
Therefore, any reasonable person believing in entropic gravity will automatically call gravity an emergent phenomenon. They must conclude that there is a new, fundamental theory of gravity to be found, and this theory will "restore" the probabilistic interpretation of entropy.
The reason entropic gravity is exciting and exotic is that many other searches for this fundamental theory start with a (more or less) direct quantization of gravity, much like one can quantize classical mechanics to arrive at quantum mechanics. Entropic gravity posits that this is the wrong approach, in the same way that one does not try to directly quantize the ideal gas law.
[0] Let me stress this: there is no entropy without probability distributions, even in physics. Anyone claiming otherwise is stuck in the nineteenth century, perhaps because they learned only thermodynamics but not statistical mechanics.
Sure, I'm not denying that entropy exists as a concept, that can be used to explain things macroscopically. But like you said, it's origins are statistical. To me, temperature is also a similar "made up" concept. We can only talk about temperature, because a sufficiently large group of particles will converge to a single-parameter distribution with their velocities. A single particle in isolation doesn't have a temperature.
So if they say gravity might be an entropic effect, does that mean that they assume there's something more fundamental "underneath" spacetime that - in the statistical limit - produces the emergent phenomenon of gravity? So it isn't the entropy of matter that they talk about, but the entropy of something else, like the grains of spacetime of whatever.
> You are absolutely right that entropy is always fundamentally a way to describe are our lack of perfect knowledge of the system [0].
> [0] Let me stress this: there is no entropy without probability distributions, even in physics.
The second item doesn't entail the first. Probabilities can be seen as a measure of lack of knowledge about a system, but it isn't necessarily so. A phenomenon can also be inherently/fundamentally probabilistic. For example, wave function collapse is, to the best of our knowledge, an inherently non-deterministic process. This is very relevant to questions about the nature of entropy - especially since we have yet to determine if it's even possible for a large system to be in a non-collapsed state.
If it turns out that there is some fundamental process that causes wave function collapse even in perfectly isolated quantum systems, then it would be quite likely that entropy is related to such a process, and that it may be more than a measure of our lack of knowledge about the internal state of a system, and instead a measurement of the objective "definiteness" of that state.
I am aware that objective collapse theories are both unpopular and have some significant hurdles to overcome - but I also think that from a practical perspective, the gap between the largest systems we have been able to observe in pure states versus the smallest systems we could consider measurement devices is still gigantic and leaves us quite a lot of room for speculation.
Entropy isn't a function of imperfect knowledge. It's a function of the possible states of a system and their probability distributions. Quantum mechanics assumes, as the name implies, that reality at the smallest level can be quantised, so it's completely appropriate to apply entropy to describing things at the microscopic scale.
If we knew the exact state of all particles in an enclosed system, we can calculate what future states will be exactly. No need to calculate possible states.
Entropy is certainly a physical “thing”, in the sense that it affects the development of the system. You can equally well apply your argument that it isn’t a physical thing because it doesn’t exist on a microscopic scale to temperature. Temperature doesn’t exist when you zoom in on single particles either.
There’s no reason to involve our knowledge of the system. Entropy is a measure of the number of possible micro states for a given system, and that number exists independently of us.
Exactly! Temperature isn't fundamental. It's a statistical measure made up by humans. It's certainly a very useful abstraction but it isn't a fundamental property. It describes an emergent pattern observed in larger systems. Same for entropy (and also AFAIK angular momentum).
It's entirely possible I'm wrong about any of the above but if so I've yet to encounter a convincing line of reasoning.
> Entropy is a measure of the number of possible micro states for a given system, and that number exists independently of us.
That number also exists independently of the system! I can imagine any system and calculate the corresponding number.
(And for an even more philosophical question, does the “system” really exist independently of us? What separates the “system” from anything else? Is every subset of the universe a “system”?)
Something to consider is that entropy has units of measure. Why would a purely philosophical concept be given units of Joules per Kelvin?
I'm only reminded about this because, though I'm a physicist, I've been out of school for more than 3 decades, and decided that I owed myself a refresher on thermodynamics. This coincided with someone on HN recommending David Tong's textbook-quality lecture notes:
I think at least the first few pages are readable to a layperson, and address the issue of our imperfect knowledge of the precise configuration of a system containing, say, 1e23 particles.
But if we knew all of those relationships, the system would still have entropy.
This comment thread is exhibit N-thousand that "nobody really understands entropy". My basic understanding goes like this:
In thermodynamics, you describe a system with a massive number of microstates/dynamical variable according to 2-3 measurable macrostate variables. (E.g. `N, V, E` for an ideal gas.)
If you work out the dynamics of those macrostate variables, you will find that (to first order, i.e. in the thermodynamic limit) they depend only on the form of the entropy function of the system `S(E, N, V)`, e.g. Maxwell relations.
If you measured a few more macrostate variables, e.g. the variance in energy `sigma^2(E)` and the center of mass `m`, or anything else, you would be able to write new dynamical relations that depend on a new "entropy" `S(E, N, V, sigma^2(E), m)`. You could add 1000 more variables, or a million—e.g every pixel of an image—basically up until the point where the thermodynamic limit assumptions cease to hold.
The `S` function you'd get will capture the contribution of every-variable-you're-marginalizing-over to the relationships between the remaining variables. This is the sense in which it represents "imperfect knowledge". Entropy dependence arises mathematically in the relationships between macrostate variables—they can only couple to each by way of this function which summarizes all the variables you don't know/aren't measuring/aren't specifying.
That this works is rather surprising! It depends on some assumptions which I cannot remember (on convexity and factorizeabiltiy and things like that), but which apply to most or maybe all equilibrium thermodynamic-scale systems.
For the ideal gas, say, the classical-mechanics, classical-probability, and quantum-mechanic descriptions of the system all reduce to the same `S(N, V, E)` function under this enormous marginalization—the most "zoomed-out" view of their underlying manifold structures turns out to be identical, which is why they all describe the same thing. (It is surprising that seemingly obvious things like the size of the particles would not matter. It turns out that the asymptotic dynamics depend only on the information theory of the available "slots" that energy can go into.)
All of this appears as an artifact of the limiting procedure in the thermodynamic limit, but it may be the case that it's more "real" than this—some hard-to-characterize quantum decoherence may lead to this being not only true in an extraordinarily sharp first-order limit, but actually physically true. I haven't kept up with the field.
Entropy can be defined as the logarithm of the number of microstates in a macrostate. Since transition between microstates is reversible, and therefore one-to-one (can't converge on any particular microstate, can't go in cycles, have to be something like a random walk) we're more likely to end up in a macrostate that holds a larger number of microstates.
For example, there are many more ways your headphone cord can be tangled than untangled, so when you pull it out of your pocket, and it's in a random state, then it's very likely to be tangled.
If entropy causes gravity, that means there are more somehow more microstates with all the mass in the universe smooshed together than microstates with all the mass in the universe spread apart.
Even if we take that view, gravity is still basically a similar case. What we call "gravity" is really an apparent force, that isnt a force at all when seen from a full 4d pov.
Imagine sitting outside the whole universe from t=0,t=end and observing one whole block. Then the trajectories of matter, unaffected by any force at all, are those we call gravitational.
From this pov, it makes a lot more sense to connect gravity with some orderly or disorderly features of these trajectories.
Inertia, on this view, is just a kind of hysteresis the matter distribution of the universe has -- ie., a kind of remembered deformation that persists as the universe evolves.
> From this pov, it makes a lot more sense to connect gravity with some orderly or disorderly features of these trajectories.
On the contrary, entropic gravity works pretty well for the Newtonian view of gravity as a force, and not the GR view of gravity as a deformation of space time and analogous to acceleration. Acceleration is a very elementary concept, one you find even in microscopic descriptions. Gravity being essentially the same thing makes it far more elementary than a concept like entropy, which only applies to large groups of particles.
So, if the GR picture is the right one, if gravity and acceleration are essentially the same thing, its very hard to see how that aligns with gravity being an emergent phenomenon that only happens at large scales. However, if gravity is just a tendency for massive objects to come together, as in the Newtonian picture, that is perfectly easy to imagine as an entropic effect.
If you want to only have one possible past (i.e. can't destroy information) then when you end up in one branch of quantum state you need to "store" enough information to separate you form other branches and you really do need to have multiple possible microstates to differentiate them. If you look post-factum obviously you did end up in a specific state, but statistics do their work otherwise.
For years I thought the same for entropy. But now I believe it is fundamentaly impossible to know each micro state, irrespective our tools and methods. And this happens like and due to Heisenberg's uncertainty principle.
So all events are irreversible and entropy is always increasing. Perfection is only theoretical.
Entropy is complicated beyond just a Rankine or Carnot cycle.
Biology thrives at the ebbs, flows, and eddies of entropy. Predation. Biochemical flux. There are arrows flowing every which way, and systems that keep it finely tuned.
This theory, based on my surface level reading and understanding, is that the aggregate particle-level entropy within sub light speed systems creates gravity.
I’ve been a believer in entropic gravity for a long time and believe it’s due to quantum foam. In a region of space with nothing in it the quantum foam in that space would be perfectly uniformly random. With mass and energy the state of the space would be biased and less random. This creates an entropic gradient. Further this doesn’t just explain gravity but explains why the space between galaxies seems to demonstrate negative energy and space expansion. I’m glad to see more research into the idea of entropic gravity as it’s IMO a more reasonable explanation than most other gravity theories I’ve heard.
We all know that life on Earth gets it's energy from the Sun.
But we also know that's an approximation we tell kids, really life gets low entropy photons from the Sun, does it's thing, and then emits high entropy infrared waste heat. Energy is conserved, while entropy increases.
But where did the Sun got it's low entropy photons to start with? From gravity, empty uniform space has low entropy, which got "scooped up" as the Sun formed.
Your question fascinated me. Googling "where did the Sun got its low entropy" I also came across these explanations:
"Solar energy at Earth is low-entropy because all of it comes from a region of the sky with a diameter of half a degree of arc."
also, from another reply:
"Sunlight is low entropy because the sun is very hot. Entropy is essentially a measure of how spread out energy is. If you consider two systems with the same amount of thermal energy, then the one where that energy is more concentrated (low entropy) will be hotter."
Probably it's a bit of both. I'm not sure I understand your hypothesis about the Sun scooping up empty, low-entropy space. Wasn't it formed from dusts and gases created by previous stellar explosions, i.e. the polar opposite of low entropy?
I read the gravity explanation for the sun low entropy in the "Road to Reality" book from Roger Penrose. Asked Gemini to summarize the argument (scroll to end)
This is just a question about the origins of inhomogeneity in the universe. The prevailing theory is cosmic inflation, I believe: in the early universe a quantum field existed in a high entropy state and then the rapid expansion of space magnified small spatial inhomogeneities in the field into large-scale structures. What we see as "low entropy" structures like stars are actually just high entropy, uniform structures at a higher scale but viewed from up close so that we can see finer-scale structure.
But where did the Sun got it's low entropy photons to start with? From gravity, empty uniform space has low entropy, which got "scooped up" as the Sun formed.
From the Big Bang originally. We don’t know what caused the Big Bang.
It's a fascinating idea that gravity could be an emergent result of how information works in the universe. I feel like we still don't have that clear piece of evidence where this model predicts something different from general relativity. For now it is one of those theories that are fun to explore but still hard to fully accept.
the statistical mechanical definition of entropy relies on the number of possible arrangements of particles in a system. In a closed system entropy approaches an equilibrium which has been sensationally described as the 'heat death of the universe'. But since we know our universe is expanding, the number of possible arrangements is also increasing so entropy may never reach equilibrium. If the universe is expanding faster than its components redistribute, then entropy could be decreasing. With this in mind, any theory involving entropy as a component of gravity would suggest a changing gravity over time
Readit News
From what I understand, this is because larger objects have more mass, moving slower when shaked, so as the larger (brazil nuts) don't move as much relative to the smaller ones (peanuts), and because of gravity, there's a cavity left under the brazil nut which gets filled in with peanuts.
For entropic gravity, the idea is that there's a base density of something (particles? sub-atomic particles?) hitting objects in random ways from all directions. When two large massive objects get near each other, their middle region will have lower density thus being attracted to each other from particles hit with less frequency from the lower density region. They sort of cast a "shadow".
I'm no physicist but last time I looked into it there were assumptions about the density of whatever particle was "hitting" larger massive objects and that density was hard to justify. Would love to hear about someone more knowledgeable than myself that can correct or enlighten me.
As an aside, the brazil nut effect is a very real effect. To get the raisins, you shake the raisin bran. To get gifts left from your cat, you shake the kitty litter. It works surprisingly well.
[0] https://en.wikipedia.org/wiki/Granular_convection
[1] https://www.youtube.com/watch?v=Incnv2CfGGM
"Many mechanisms for gravitation have been suggested. It is interesting to consider one of these, which many people have thought of from time to time. At first, one is quite excited and happy when he “discovers” it, but he soon finds that it is not correct. It was first discovered about 1750. Suppose there were many particles moving in space at a very high speed in all directions and being only slightly absorbed in going through matter. When they are absorbed, they give an impulse to the earth. However, since there are as many going one way as another, the impulses all balance. But when the sun is nearby, the particles coming toward the earth through the sun are partially absorbed, so fewer of them are coming from the sun than are coming from the other side. Therefore, the earth feels a net impulse toward the sun and it does not take one long to see that it is inversely as the square of the distance—because of the variation of the solid angle that the sun subtends as we vary the distance. What is wrong with that machinery? It involves some new consequences which are not true. This particular idea has the following trouble: the earth, in moving around the sun, would impinge on more particles which are coming from its forward side than from its hind side (when you run in the rain, the rain in your face is stronger than that on the back of your head!). Therefore there would be more impulse given the earth from the front, and the earth would feel a resistance to motion and would be slowing up in its orbit. One can calculate how long it would take for the earth to stop as a result of this resistance, and it would not take long enough for the earth to still be in its orbit, so this mechanism does not work. No machinery has ever been invented that “explains” gravity without also predicting some other phenomenon that does not exist."
I get this is vague spitballing but essentially an ‘action potential’ would allow mass to move. Higher temperature mass interacts more, lower temperature interacts less. Mass with momentum would be biased to absorb more from one side so it travels in a specific direction in space more than others (the idea i’m getting at is that all movement in space only occurs with interaction with this field), this also would counteract issues with moving mass interacting more on a specific side - the very bias of mass with momentum to absorb more on one side means that from that masses point of view it has the same action potentials interacting from all sides. Mass shielded behind mass receives fewer action potentials so experiences exactly the effect that you can call time dilation. Mass shielding other mass from action potentials also means that mass accelerates towards other mass.
Essentially its the above but instead of a massive particle hitting other mass from all sides it’s a field that allows mass to experience a unit of time.
Would this be true if the speed of particles is constant in all frames of reference?
Deleted Comment
At lower speeds you get something akin to Newtonian gravity but at higher velocities you get something resembling MOND gravity where galaxies clusters and large voids appear - no dark matter needed.
https://www.youtube.com/watch?v=HKvc5yDhy_4
For example if I were to roll the chamber at a very low frequency, I would expect the particles to clump on one side, then the other and so on. This is not really so surprising and the frequency will depend on the chamber dimensions.
https://en.wikipedia.org/wiki/Rubber_band_experiment
"The stretching of the rubber band is an isobaric expansion (A → B) that increases the energy but reduces the entropy"
[apologies for any reversed signs below, I think I caught them all]
In Verlinde' entropic gravity, there is a gravitational interaction that "unstretches" the connection between a pair of masses. When they are closer together they are at higher entropy than when they are further apart. There is a sort of tension that drags separated objects together. In Carney et al's approach there is a "pressure mediated by a microscopic system which is driven towards extremization of its free energy", which means that when objects are far apart there is a lower entropy condition than when they are closer together, and this entropy arises from a gas with a pressure which is lower when objects are closer together than when objects are further apart. Pressure is just the inverse of tension, so at a high enough level, in both entropic gravity theories, you just have a universal law -- comparable to Newton's -- where objects are driven (whether "pulled" or "pushed") together by an entropic force.
This entropic force is not fundamental - it arises from the statistical behaviour of quantum (or otherwise microscopic) degrees of freedom in a holographic setting (i.e., with more dimensions than 3+1). It's a very string-theory idea.
The approach is very hard to make it work unless the entropic force is strictly radial, and so it's hard to see how General Relativity (in the regime where it has been very well tested) can emerge.
The paper cannot deal with fast-moving masses at all: it's not just the relativstic regime (where speeds are significant fractions of c) but rather the masses must move more slowly than the thermalization. This is hugely restrictive.
Finally, comparing themselves to the traditional approach of quantizing perturbations (e.g. turning classical (General Relativity) gravitational waves into lots of spin-2 gravitons) the authors write:
They also say that while their starting point was being very different from the holographic picture: Some of this will necessarily by driven by the need to be compatible with General Relativity in the weak field limit. They are not compatible with strong gravity in General Relativity at present.So while the idea is kinda interesting, I think they are putting the cart before the horse in asking what their model says about things like the interaction between gravitation and entanglement. That's simply unmeasurable by experiment right now whereas the very-well-understood relativistic precession of Mercury's perihelion is completely out of scope for this initial paper.
That doesn’t make sense to me. If larger objects move slower, don’t they move faster relative to the (accelerating) reference frame of the container?
Also, conventional wisdom has it that shaking (temporarily) creates empty spaces, and smaller objects ‘need’ smaller such spaces to fall down, and thus are more likely to fall down into such a space.
Yes? But so what? The relevant interaction is between the peanuts and the Brazil it's.
> Also, conventional wisdom has it that shaking (temporarily) creates empty spaces, and smaller objects ‘need’ smaller such spaces to fall down, and thus are more likely to fall down into such a space.
Right, but preferentially under the larger Brazil nuts.
I always thought it was because the smaller nuts can fall into smaller spaces, while the larger nuts cannot.
Like yes, when we look at earth from incredibly far away, it's a pale blue dot. But all those oceans on it are flowing and separate from the solid ground underneath. Those large boulders on earth that would have their own (tiny) gravitational pull on their own in space are just part of earth's single gravitational force. All the airplanes in the sky are subject to the pull of the earth, but they're also a part of the gravitational pull that pulls other things to earth.
When shaking cereal, the big flakes rise to the top, but tiny bits of dust from each flake also separates and settle at the bottom. But earth, as a whole, has big bits and little bits everywhere all flowing freely. And gravity seemingly treats all those bits as a single object. But with sufficient distance between objects (e.g. different planets), it treats them separately. And with greater distance (e.g. galactic scale), it treats them as one again.
It does not; but when you learned about gravity in school or wherever, you were only presented with scenarios in which it was valid to do so. Specifically, for Newtonian gravity, an object whose density is spherically symmetrical may be treated as a point mass at its center (w/r/t other point masses farther from the center than any point in the first object); this can be seen by integrating Newton's equation.
There's no reason to attribute this to special behavior by gravity with respect to "objects" which you identify. You could decompose a (spherically symmetrical) mass into several different spherically symmetrical "objects" and sum up their influence on a test mass, and the result is the same as if you had treated the original mass as a point mass. The hypothesis that gravity is "treating" the object one way or another now fails to distinguish all these possibilities; it's no longer physically meaningful.
At sufficiently large distances, or for sufficiently large ratio of large to small mass, the difference between, say, a planet and a spherically symmetrical mass is so small with respect to the main effect that it can simply be ignored.
Understanding the tides depends very much on disabusing oneself of this scaffolding.
One of those unintuitive results.
It probably only works in classical gravity but it’s still neat.
For example, if you flip N coins, there are 2^N states available once the flip is done. Each outcome has an 1/2^N probability of outcome. There's only one state where all of the states show all heads. While there's only one state where coins numbers 1-N/2 are heads, and N/2-N are tails, so that particular outcome is 1/2^N, if all we care is the macroscopic behavior of "how many heads did we get"--we'll see that we got "roughly" N/2 heads especially as N gets larger.
Entropy is simply saying there's a tendency towards these macroscopically likely groups of states.
Actually this is currently blowing my mind: does the (usual intro QM) wavefunction only describe the probability amplitude for the position of a particle when using photon interaction to measure, and actually a particle's "position" would be different if we used e.g. interaction with a Z boson to define "position measurement"?
As the position wavefunction is now completely determined in a probe-agnostic matter, it would be hard to justify calling a probe that didn't yield the corresponding probability distribution a “position measurement”.
are all celestial bodies then a local up and 'away from them' down?
this analogy hurts my brain. please tell me how to make the hurting stop
But there are so many potential assumptions baked into these theories that it's hard to believe when they claim, "look, Einstein's field equations."
I agree.
> and that the global and exquisitly weak force of gravity emerges from that theory as a sort of accounting error.
Nah, it's probably just another weird family of bosons, just like the other forces.
From the article:
> Entropic gravity is very much a minority view. But it’s one that won’t die, and even detractors are loath to dismiss it altogether.
The metrics attempt to balance the ability of a model to fit data with the number of parameters required. For equally well-fitting models, they prefer the one with fewer params.
If Wolfram's theory fits as well but has fewer params, it should be preferred. I'm not sure if fewer "concepts" counts, but it's something to consider.
Dead Comment
Which kinda points to the fact that we’re not smart enough to make these steps without “hints”. It’s quite possible that our way of working will lead to a theory of everything in the asymptote, when everything is observed.
My favorite conjecture is that what happens is things effectively lose a dimension when they reach the EH surface, and become like a "flatlander" (2D) universe, having only two degrees of freedom on the surface. For such a 2D universe their special "orthogonal" dimension they'd experience as "time" is the surface normal vector. Possibly time only moves forward for them when something new "falls in" causing the sphere to expand.
This view of things also implies the Big Bang is wrong, if our universe is a 3D EH. Because if you roll back the clock on an EH back to when it "formed" you don't end up at some distant past singularity; you simply get back to a time where stuff began to clump together from higher dimensions. The universe isn't exploding from a point, it's merely expanding because it itself is a 3D version of what we know as Event Horizons.
Just like a fish can't tell it's in water, we can't tell we're on a 3D EH. But we can see 2D versions of them embedded in our space.
To me, entropy is not a physical thing, but a measure of our imperfect knowledge about a system. We can only measure the bulk properties of matter, so we've made up a number to quantify how imperfect the bulk properties describe the true microscopic state of the system. But if we had the ability to zoom into the microscopic level, entropy would make no sense.
So I don't see how gravity or any other fundamental physical interaction could follow from entropy. It's a made-up thing by humans.
Physical entropy governs real physical processes. Simple example: why ice melts in a warm room. More subtle example: why cords get tangled up over time.
Our measures of entropy can be seen as a way of summarizing, at a macro level, the state of a system such as that warm room containing ice, or a tangle of cables, but the measure is not the same thing as the phenomenon it describes.
Boltzmann's approach to entropy makes the second law pretty intuitive: there are far more ways for a system to be disordered than ordered, so over time it tends towards higher entropy. That’s why ice melts in a warm room.
Entropy isn’t always the driver of physical change, sometimes it’s just a map.
Sometimes that map is highly isomorphic to the physical process, like in gas diffusion or smoke dispersion. In those cases, entropy doesn't just describe what happened, it predicts it. The microstates and the probabilities align tightly with what’s physically unfolding. Entropy is the engine.
But other times, like when ice melts, entropy is a summary, not a cause. The real drivers are bond energies and phase thresholds. Entropy increases, yes, but only because the system overcame physical constraints that entropy alone can’t explain. In this case, entropy is the receipt, not the mechanism.
So the key idea is this: entropy’s usefulness depends on how well it “sees” the real degrees of freedom that matter. When it aligns closely with the substrate, it feels like a law. When it doesn't, it’s more like coarse bookkeeping after the fact.
The second law of thermodynamics is most “real” when entropy is the process. Otherwise, it’s a statistical summary of deeper physical causes.
I'm a complete layman when it comes to physics, so forgive me if this is naive — but aren't "ordered" and "disordered" concepts tied to human perception or cognition? It always seemed to me that we call something "ordered" when we can find a pattern in it, and "disordered" when we can't. Different people or cultures might be able to recognize patterns in different states. So while I agree that "there are more ways for a system to be disordered than ordered," I would have thought that's a property of how humans perceive the world, not necessarily a fundamental truth about the universe
Maybe it would be more fitting to say that it just so happens that our human definition of “messy” aligns with entropy, and not that someone decided what messy atoms look like.
I’d say a bucket of water is more neat than a bucket of ice, macroscopically.
Ice melting is simply the water molecules gaining enough kinetic energy (from collisions with the surrounding air molecules) that they break the bonds that held them in the ice crystal lattice. But at the microscopic level it's still just water molecules acting according to Newton's laws of motion (forgetting about quantum effects of course).
Now, back on the topic of the article: consider a system of 2 particles separated by some distance. Do they experience gravity? Of course they do. They start falling towards the midpoint between them. But where is entropy in this picture? How do you even define entropy for a system of 2 particles?
Physical processes are "real", but entropy is a figment.
Deleted Comment
> the measure is not the same thing as the phenomenon it describes.
There is some tension between those claims.
The latter seems to support the parent comment’s remark questioning whether a “fundamental physical interaction could follow from entropy”.
It seems more appropriate to say that entropy follows from the physical interaction - not to be confused with the measure used to describe it.
One may say that pressure is an entropic force and physical entropy governs the real physical process of gas expanding within a piston.
However, one may also say that it’s the kinetic energy of the gas molecules what governs the physical process - which arguably is a more fundamental and satisfactory explanation.
Nevertheless there is a distinct "reality" to entropic forces, in the sense that it is something that can actually be measured in the lab. If you are not convinced then you can look at:
https://en.wikipedia.org/wiki/Entropic_force
and in particular the example that is always used in a first class on this topic:
https://en.wikipedia.org/wiki/Ideal_chain
So when viewed in this way entropy is not just a "made-up thing", but an effective way to describe observed phenomena. That makes it useful for effective but not fundamental laws of physics. And indeed the wiki page says that entropic forces are an "emergent phenomenon".
Therefore, any reasonable person believing in entropic gravity will automatically call gravity an emergent phenomenon. They must conclude that there is a new, fundamental theory of gravity to be found, and this theory will "restore" the probabilistic interpretation of entropy.
The reason entropic gravity is exciting and exotic is that many other searches for this fundamental theory start with a (more or less) direct quantization of gravity, much like one can quantize classical mechanics to arrive at quantum mechanics. Entropic gravity posits that this is the wrong approach, in the same way that one does not try to directly quantize the ideal gas law.
[0] Let me stress this: there is no entropy without probability distributions, even in physics. Anyone claiming otherwise is stuck in the nineteenth century, perhaps because they learned only thermodynamics but not statistical mechanics.
So if they say gravity might be an entropic effect, does that mean that they assume there's something more fundamental "underneath" spacetime that - in the statistical limit - produces the emergent phenomenon of gravity? So it isn't the entropy of matter that they talk about, but the entropy of something else, like the grains of spacetime of whatever.
> [0] Let me stress this: there is no entropy without probability distributions, even in physics.
The second item doesn't entail the first. Probabilities can be seen as a measure of lack of knowledge about a system, but it isn't necessarily so. A phenomenon can also be inherently/fundamentally probabilistic. For example, wave function collapse is, to the best of our knowledge, an inherently non-deterministic process. This is very relevant to questions about the nature of entropy - especially since we have yet to determine if it's even possible for a large system to be in a non-collapsed state.
If it turns out that there is some fundamental process that causes wave function collapse even in perfectly isolated quantum systems, then it would be quite likely that entropy is related to such a process, and that it may be more than a measure of our lack of knowledge about the internal state of a system, and instead a measurement of the objective "definiteness" of that state.
I am aware that objective collapse theories are both unpopular and have some significant hurdles to overcome - but I also think that from a practical perspective, the gap between the largest systems we have been able to observe in pure states versus the smallest systems we could consider measurement devices is still gigantic and leaves us quite a lot of room for speculation.
There are no probability distributions over possible states when there is perfect knowledge of the state.
> Quantum mechanics
Entropy is also zero for a pure quantum state. You won’t have entropy without imperfect knowledge.
There’s no reason to involve our knowledge of the system. Entropy is a measure of the number of possible micro states for a given system, and that number exists independently of us.
It's entirely possible I'm wrong about any of the above but if so I've yet to encounter a convincing line of reasoning.
That number also exists independently of the system! I can imagine any system and calculate the corresponding number.
(And for an even more philosophical question, does the “system” really exist independently of us? What separates the “system” from anything else? Is every subset of the universe a “system”?)
I'm only reminded about this because, though I'm a physicist, I've been out of school for more than 3 decades, and decided that I owed myself a refresher on thermodynamics. This coincided with someone on HN recommending David Tong's textbook-quality lecture notes:
https://www.damtp.cam.ac.uk/user/tong/statphys.html
I think at least the first few pages are readable to a layperson, and address the issue of our imperfect knowledge of the precise configuration of a system containing, say, 1e23 particles.
But if we knew all of those relationships, the system would still have entropy.
In thermodynamics, you describe a system with a massive number of microstates/dynamical variable according to 2-3 measurable macrostate variables. (E.g. `N, V, E` for an ideal gas.)
If you work out the dynamics of those macrostate variables, you will find that (to first order, i.e. in the thermodynamic limit) they depend only on the form of the entropy function of the system `S(E, N, V)`, e.g. Maxwell relations.
If you measured a few more macrostate variables, e.g. the variance in energy `sigma^2(E)` and the center of mass `m`, or anything else, you would be able to write new dynamical relations that depend on a new "entropy" `S(E, N, V, sigma^2(E), m)`. You could add 1000 more variables, or a million—e.g every pixel of an image—basically up until the point where the thermodynamic limit assumptions cease to hold.
The `S` function you'd get will capture the contribution of every-variable-you're-marginalizing-over to the relationships between the remaining variables. This is the sense in which it represents "imperfect knowledge". Entropy dependence arises mathematically in the relationships between macrostate variables—they can only couple to each by way of this function which summarizes all the variables you don't know/aren't measuring/aren't specifying.
That this works is rather surprising! It depends on some assumptions which I cannot remember (on convexity and factorizeabiltiy and things like that), but which apply to most or maybe all equilibrium thermodynamic-scale systems.
For the ideal gas, say, the classical-mechanics, classical-probability, and quantum-mechanic descriptions of the system all reduce to the same `S(N, V, E)` function under this enormous marginalization—the most "zoomed-out" view of their underlying manifold structures turns out to be identical, which is why they all describe the same thing. (It is surprising that seemingly obvious things like the size of the particles would not matter. It turns out that the asymptotic dynamics depend only on the information theory of the available "slots" that energy can go into.)
All of this appears as an artifact of the limiting procedure in the thermodynamic limit, but it may be the case that it's more "real" than this—some hard-to-characterize quantum decoherence may lead to this being not only true in an extraordinarily sharp first-order limit, but actually physically true. I haven't kept up with the field.
No idea how to apply this to gravity though.
For example, there are many more ways your headphone cord can be tangled than untangled, so when you pull it out of your pocket, and it's in a random state, then it's very likely to be tangled.
If entropy causes gravity, that means there are more somehow more microstates with all the mass in the universe smooshed together than microstates with all the mass in the universe spread apart.
Imagine sitting outside the whole universe from t=0,t=end and observing one whole block. Then the trajectories of matter, unaffected by any force at all, are those we call gravitational.
From this pov, it makes a lot more sense to connect gravity with some orderly or disorderly features of these trajectories.
Inertia, on this view, is just a kind of hysteresis the matter distribution of the universe has -- ie., a kind of remembered deformation that persists as the universe evolves.
On the contrary, entropic gravity works pretty well for the Newtonian view of gravity as a force, and not the GR view of gravity as a deformation of space time and analogous to acceleration. Acceleration is a very elementary concept, one you find even in microscopic descriptions. Gravity being essentially the same thing makes it far more elementary than a concept like entropy, which only applies to large groups of particles.
So, if the GR picture is the right one, if gravity and acceleration are essentially the same thing, its very hard to see how that aligns with gravity being an emergent phenomenon that only happens at large scales. However, if gravity is just a tendency for massive objects to come together, as in the Newtonian picture, that is perfectly easy to imagine as an entropic effect.
So all events are irreversible and entropy is always increasing. Perfection is only theoretical.
Deleted Comment
Biology thrives at the ebbs, flows, and eddies of entropy. Predation. Biochemical flux. There are arrows flowing every which way, and systems that keep it finely tuned.
This theory, based on my surface level reading and understanding, is that the aggregate particle-level entropy within sub light speed systems creates gravity.
All of physics is made up by humans.
But we also know that's an approximation we tell kids, really life gets low entropy photons from the Sun, does it's thing, and then emits high entropy infrared waste heat. Energy is conserved, while entropy increases.
But where did the Sun got it's low entropy photons to start with? From gravity, empty uniform space has low entropy, which got "scooped up" as the Sun formed.
EDIT: not sure why this is downvoted, is the explanation Nobel Physics laureate Roger Penrose gives: https://g.co/gemini/share/bd9a55da02b6
"Solar energy at Earth is low-entropy because all of it comes from a region of the sky with a diameter of half a degree of arc."
also, from another reply:
"Sunlight is low entropy because the sun is very hot. Entropy is essentially a measure of how spread out energy is. If you consider two systems with the same amount of thermal energy, then the one where that energy is more concentrated (low entropy) will be hotter."
https://physics.stackexchange.com/questions/796434/why-does-...
Probably it's a bit of both. I'm not sure I understand your hypothesis about the Sun scooping up empty, low-entropy space. Wasn't it formed from dusts and gases created by previous stellar explosions, i.e. the polar opposite of low entropy?
https://g.co/gemini/share/bd9a55da02b6
The photons from Sun are hot, the space around Sun is cold, the system has a low entropy.
If the space around Sun was as hot as the photons, the entropy would be high.
"It's turtles all the way down."