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According to the second law of thermodynamics, the entropy of a closed system increases (or in energy terms, the Gibbs free energy decreases, or in temperature language, the temperature tends to the same value over the system).

This means that the intial state of the universe was a low entropy one. This question is about the problem how a gaseous hot state can be in a low entropy state. It is argued that because of gravity it's actually a low entropy state as compared to a state filled with black hole reservoirs.

Now the initial state was not a gas made up from neutral particles. It's made up of neutrons, neutrinos, protons, and electrons, all having a high kinetic energy.

In time, the low entropy state tends to higher entropy, be it because of gravity, the other three forces or expansion. You could say that exactly that evolution constitutes time. The Gibbs free energy is reduced, gravitation-induced structures arise (which, somewhat counterintuitively, increases the entropy), and life evolves.

It seems a pretty straightforward process. From low, to high entropy. The structured appearance that emerges in time seems to be at odds with the second law, but the total entropy still increases. I do not understand what the initial low entropy state problem is. Why is that a problem?

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I think you characterize very well everything. The question is why worry about the low-entropy IC of the early universe. The answer, roughly stated, is that it is the opposite one would expect the universe to be at the early universe. Physical systems (considering gravitation or not, doesn't matter) have many many more microstates corresponding to the high-entropy equilibrium macrostate. If you were to pick randomly, by chance, arbitrarily (state it as you wish) a microstate as an Initial Condition, then it would be extremely extremely unlikely that you pick a low-entropy microstate.

The CMB confirms that low-entropy initial state (assuming the gravitational considerations). This empirical confirmation doesn't make it less surprising.

Penrose (e.g. in "Cycles of time") explains this clearly and makes a rough quantification of how extremely unlikely it would be.

This problem has also been associated to the fine-tuning problems, as it seems to exhibit the same structure.

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  • $\begingroup$ Yes, that's the so-called "problem": IF you chose an initial state at random, from a coarse-graining that includes gravitational degrees of freedom, you don't get a state that looks like the early universe. The baffling thing is that many people think that it makes sense to choose an initial state at random, and that such randomness would be any sort of "explanation". Choosing at random is done when you don't have anything interesting to explain, when all choices are thought to have an equal a priori likelihood. Clearly that's the wrong sort of logic to be using in this context. $\endgroup$ Jul 19, 2023 at 20:24
  • $\begingroup$ Exactly. The implicit assumption of an "a priori" uniform probability distribution among possible IC is disputed. Philosophers have criticized fine-tuning arguments along the same lines. However, I'm personally unconvinced that these values are not surprising and don't need explanation. I agree the uniform probability is unjustified, but it seems suspicious to me that only few biased distributions lead to the needed values. Maybe if the distribution is not in terms of chances of IC, but in terms of objective expectations of an ideal rational agent, the problem becomes more well posed. $\endgroup$ Jul 19, 2023 at 21:03
  • $\begingroup$ Yes, it certainly needs an explanation, but not a "random explanation" or a dynamic explanation. It needs a "boundary explanation". Here's an essay I wrote on the topic a few years back. forums.fqxi.org/d/3139-fundamental-is-non-random-by-ken-wharton $\endgroup$ Jul 20, 2023 at 1:03

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