Why thermodynamic arrow of time will not reverse during the big crunch (considering our universe is above the critical mass)?

Question

As the question states, Why thermodynamic arrow of time will not reverse during the big crunch (considering our universe is above the critical mass)?

The doubt arised because I thought the cosmological arrow of time is linked to the thermodynamical arrow of time, because in the big crunch the thermodynamical free energy becomes negligible (actually according to Gibbs free energy in a reversible system, if the total temperature is like a quark gluon plasma focused at a singularity, we may find entropy at the big crunch by using relation between higgs free energy and entropy however I was unable to find the equation), this signify that they both are somehow linked, and the big bang was the start of entropy

I know that according to CPT symmetry, in any case the laws of physics, in this case 2nd law of thermodynamics shan't be reversed and must abide therefore time (since psychological time is linked to thermodynamical time) shall not be reversed

But due to what mechanism this happens (usually if a thing causes entropy of the system to decrease, some process counters that and leads to increase in the total entropy)?

Note: This would be considering our universe has sufficient mass-cosmological constant proportion that big crunch could occur, now maybe this is linked to the anthropotic principle and because of this the mass distribution is so finetuned, but maybe according to superposition this could occur in someone else's universe without changing the CPT symmetry or physical laws

Answer 1

In the Bayesian view, entropy characterizes the observer's knowledge about the system. Paradoxes arise when one veers from this view. Quoting Jaynes, Information Theory and Statistical Mechanics II (1957),

[...] probabilities represent only our ignorance as to the true state. With such an interpretation the expression "irreversible process" represents a semantic confusion; it is not the physical process that is irreversible, but rather our ability to follow it. The second law of thermodynamics then becomes merely the statement that although our information as to the state of a system may be lost in a variety of ways, the only way in which it can be gained is by carrying out further measurements.

Jaynes makes the point that the increase of entropy represents our increasing inability to predict the state of the system as it moves further out in the future based on present knowledge–just think about predicting the weather.

The association of entropy with "disorder" is only meaningful in quasi-equilibrium. Then we can assert that the state with the maximum number of microstates (maximum "disorder") is the most likely state. But this idea doesn't carry over to non equilibrium situations.

In the context of the highly non equilibrium state during the big crunch, just as with the big bang, entropy does not refer to increasing or decreasing order, but to increasing uncertainty about making predictions too far out into the future based exclusively on present information. The weather two months out into the future is tough to predict regardless of whether it is hurricane season (a lot of disorder) or not.