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How I got interested:-

A few days ago I was watching a few YouTube videos about reversing entropy and how it was impossible.

But while thinking about it, it suddenly seemed like gravity reverses entropy.

My understanding of entropy:-

Entropy is the measurement of disorder in a system. The more disorder, the more entropy.

And the second law of thermodynamics states that entropy of a closed system must increase.

Why does it seems to me that gravity reverses entropy:-

Let's take the local group as a closed system. It is gravitationaly bounded. Exclude dark energy.

As time will pass, slowly every galaxy will start to merge with each other because of gravity.

So the local group will become more and more ordered as time passes rather than dissipating and increasing disorder.

So it seems that gravity decreases disorder, which means it reverses entropy.

Question:-

Obviously it is not likely that I have discovered something new by doing no math. So it is likely that I have missed something.

So my question is that what did I miss?

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A few days ago I was watching a few YouTube videos about reversing entropy and how it was impossible.

I think you might mean "decrease entropy", and it's perfectly possible for the entropy of a system to decrease. Only the entropy of an isolated system is required to never decrease (which you state later in your post). But the entropy decreases for plenty of non-isolated systems, e.g. a cup of room-temperature water you put in the freezer.

Entropy is the measurement of disorder in a system. The more disorder, the more entropy.

This is your issue. This is a poor qualitative and subjective understanding of entropy. A typical example of the failure of this view is stirring milk into coffee. The coffee goes from a uniform dark color, to a non-uniform mixture of coffee and milk, and then finally to a uniform lighter color. Now, the middle of this process, where you can see the milk and coffee swirling around each other, looks more disordered than the start and the end, and so you might naively think the entropy increases and then decreases in this example. However, the final uniform mixture has the highest entropy, even though it looks more ordered than the partial mixture at earlier times.

You are going purely off of body locations to determine entropy, but there is more to it than that. Entropy is more precisely defined (in one way) as the (logarithm) of the number of microstates accessible to a system. Other things, such as energy of your system, need to fully be considered in order to talk about the entropy of your system.

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  • $\begingroup$ Don't you think the intermediate state of swirling coffee looks more ordered (instead of more disordered)? $\endgroup$ Apr 1, 2021 at 6:39
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    $\begingroup$ I think the expression reversing entropy might refer to the science fiction film Tenet in which it is often used. $\endgroup$
    – Muschkopp
    Apr 1, 2021 at 8:24
  • $\begingroup$ @Muschkopp Ah, that makes some sense actually haha. I'm still not sure how I feel about that movie. $\endgroup$ Apr 1, 2021 at 8:34
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    $\begingroup$ This answer leaves the reader having to work out for himself how to apply to the question of gravitational systems. I recommend reading the other answers which tell you. $\endgroup$
    – isometry
    Apr 1, 2021 at 9:11
  • $\begingroup$ @duality The OP doesn't specify much about the system. I'm not going to speculate $\endgroup$ Apr 1, 2021 at 11:30
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When gas collapses to form a star, it will increase in temperature. If we ignore radiation and any interaction of the gas with its surroundings, this will be an adiabatic compression where entropy remains constant. The loss of entropy due to the confinement of the gas molecules into a smaller space will be offset by the increase in entropy due to the broader distribution of molecule velocities (a hotter gas has greater entropy).

The hot gas will also radiate and warm cooler objects in the environment, likely causing a net increase in entropy.

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Gravity does not reverse an increase of entropy. If a ball rolls of a shelf, gravity will pull it down, converting potential energy into kinetic energy. If the ball hits a perfectly bouncy floor, it will bounce up to the same height as before. In thermodynamics this is considered reversible because there is no change in entropy. The ball will continue to bounce to the same height forever.

In order for the ball to stop bouncing, there must be some friction. In the process of friction, the ball shares its energy with the molecules of the floor. At the beginning we have an ordered situation where all the energy is in one body (the ball.) At the end the energy is shared between the many molecules of the floor. While things may look macroscopically more ordered because the ball is now steady, at the molecular scale the situation is actually more disordered. It's statistically very unlikely (impossible even) that the molecules of the floor, which now have the energy from the ball shared between them, would ever return all the energy to the ball so that it starts bouncing again. The stopping of the ball is an irreversible process, because entropy is increased. The increased energy of the molecules of the floor is noted as a tiny increase in temperature.

In summary, gravity pulls the ball down, but without friction it will bounce right up to where it was before. Friction can cause an apparent decrease in disorder at the macroscopic scale, but this is accompanied by an increase in disorder at the molecular scale.

(Note that I thave treated the ball here as if it was infinitely hard / a single molecule. In practice, any real ball will not be be perfectly hard and bouncy, so some of kinetic energy from the ball bouncing will also be absorbed by the ball itself, resulting in disordered movement of the molecules in the ball, thus increasing its temperature too.)

Similarly, if two planets collide, gravity can only make them coalesce because friction causes kinetic energy to be converted to thermal energy, with an increase in disorder at the molecular scale. Otherwise, the planets would bounce right off each other.

Two galaxies on a collision course might (if sparse enough) pass right through each other (gravitational interactions might cause some stars to deflect.) If they coalesce, it will be because the kinetic energy due to the velocity they had relative to each other is dissipated by friction - which means an increase in entropy.

Entropy is related to the number of degrees of freedom in the system. In the initial state, entropy is low because only the ball is moving, hence low degrees of freedom. In the final state, friction has spread the energy of the ball amongst the molecules of the floor,so the energy is shared between many degrees of freedom, hence higher entropy.

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I wondered about this myself. Especially after reading a book by Brian Greene (I don't remember if it was "the elegant universe" or "The fabric of the cosmos"), in which it was stated that gravity indeed contributes negatively to unfolding chaos.

On can read here:

The first stars did not appear until perhaps 100 million years after the big bang, and nearly a billion years passed before galaxies proliferated across the cosmos. Astronomers have long wondered: How did this dramatic transition from darkness to light come about? After decades of study, researchers have recently made great strides toward answering this question. Using sophisticated computer simulation techniques, cosmologists have devised models that show how the density fluctuations left over from the big bang could have evolved into the first stars.

Here you can read:

Gravity tries to keep things together through attraction and thus tends to lower statistical entropy. The universal law of increasing entropy (2nd law of thermodynamics) states that the entropy of an isolated system that is not in equilibrium will tend to increase with time, approaching a maximum value at equilibrium.

Does this appearance of stars contradict the growth of disorder? After all, the stars, i.e., their spherical and their distribution in space (so not their constituents, which is dealt with in the above answers) show a more ordered state than you would see if all the stars were spread across the universe and their forms were non-spherical (by which I mean forms that are less ordered than spherical).

I'm inclined to say no though because in the process of star-forming, there are gravitational waves produced too and they can compensate for the increase in order (just as the radiation from the sun compensates for the increase in order on Earth). I can't offer a quantitative explanation, though, but what else would be able to compensate for the increase? It's the second law of thermodynamics I use to explain that the total gravitational order can't increase, though I'm not sure if it can be applied to gravity.

To put it differently, gravity induces a global order in the distribution pattern of matter: planet and moon shapes, star shapes, star-planets-system shapes, star cluster shapes, galaxy shapes, galaxy cluster shapes, supercluster shapes, etc. The increase in the order of the individual constituents is compensated for by electromagnetic radiation, while the increase in the "form order" is compensated for by gravitational radiation (which is so low that it is not detectable).

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There are many processes which move entropy around, so that some parts end up with less entropy than they started with, and the entropy in the other parts increases. So overall the net total entropy of the global system goes up, but it is very significant that within this there can be regions of low entropy, such as planets and living things (which have low entropy compared to a diffuse gas made of the same amount of material).

Gravitational collapse results in great and increasing contrasts: some parts dense and hot (e.g. stars); other parts cold and diffuse (e.g. intergalactic voids). So although this does not contradict the overall increase of entropy, that is not the only significant thing to note. It is also significant that this process results in structure in some regions. Rather than a uniform gas just getting more and more diffuse (a boring universe) we have pockets of gas condensing into galaxies, stars, planets, life, while other gas expands into the voids (an interesting universe).

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  • $\begingroup$ Has this actually been calculated or is it just a guess? $\endgroup$ Mar 31, 2021 at 22:33
  • $\begingroup$ @user253751 There is no guesswork in this answer; it is all standard physics. $\endgroup$ Apr 1, 2021 at 1:11
  • $\begingroup$ then can you please show the source for gravitational collapse increasing entropy rather than decreasing it\? $\endgroup$ Apr 1, 2021 at 18:18
  • $\begingroup$ @user253751 when particles move under their mutual gravitation they are following ordinary physics which is reversible and hence no entropy changes are involved in the first instance. But as they begin to undergo more complicated motions one no longer keeps track of the details of the state of all of them, and this is what entropy increase involves. Meanwhile thermal radiation of energy $Q$ from the hotter to the colder regions causes the colder regions to get $\Delta S=Q/T_c$ entropy increase while hotter reduce their entropy by $\Delta S=Q/T_h$. $\endgroup$ Apr 1, 2021 at 19:33
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Let's do some quantitative answer for those interested in more in-depth discussion. I'll just follow the discussion in Gravity, Entropy, and Cosmology: In Search of Clarity arxiv paper.

We start with a spherical volume of gas of radius $R$ that contains $N$ particles and that have total energy $E$. The standard expression for entropy of such gas is: $$S = k_bN\left[\ln\frac{V}{N} + \frac32\ln\frac{K}{N} + C \right]$$ Where $V$ is the volume, $K$ is total kinetic energy of the particles and $C$ is an irrelevant for us constant. Substituting volume and $K=E-U$: $$ S(E,R) = k_bN\left[3\ln\frac{R}{N} + \frac32\ln\frac{E-U}{N} + C' \right]$$ Where we moved all the constant stuff into $C'$.

The gravitational potential energy of the particles of mass $\mu$ each would be: $$U = - \frac35 \frac{G(\mu N)^2}{R}$$

Now, we can try to find the maximum of $S$ as a function of $R$.
Differentiating and doing some simplifications: $$ \frac{dS}{dR} = \frac{3Nk_b}{R}\left[1+\frac{U}{2K}\right] = 0$$ $$ 2 K = - U $$ So, the maximum-entropy state is reached at the radius when the potential energy is twice the kinetic energy.

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I remember I read in Thirrings book 'mathematical physics' probably vol 1 or 2. Something like this: If you have two cluster of gravitational matter at different temperature (measured by the kinetic energy, I think) and they pass through each other then we know from numerical experiment, that the cluster that was cooler before the 'collision' is even more cool afterwards and the other one hotter. So in that sense gravity leads to systems with a negative heat-capacity; but nobody has been able to prove that so far.

I think this is the interesting part of the problem. Talking about entropy here adds murkiness (difficult to define for unbound systems) and since you might not be able to run a heat engine between galaxies (even in principle) it is all a bit unclear (at least to me).

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  • $\begingroup$ Proving that a gravitational system, treated as a thermodynamic system, has a negative specific heat is a trivial exercise. The non-trivial part is to understand the consequences of this fact. $\endgroup$ Mar 31, 2021 at 21:50
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I don't see how the example of merging N galaxies to form a bigger galaxy means a decrease of disorder.

We have before a situation where stars $X_1$, $X_2$, ...,$X_n$ are in a region of space (galaxy $X$), that is completely separated from other region where stars $Y_1$, $Y_2$,...,$Y_n$ are in the galaxy $Y$.

After merging, the stars are no longer organized in different sets, but all together.

It is like taking the books of a bookstore, that are previously ordered by some criteria and put them together in a arbitrary way.

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