08/02/2022 Quick note on thermodynamics 2nd law and heat death

It isn't appear particularly convinsing to me that the second law of thermodynamics, that Entropy always increase with time, is an empirical law that lacks of actual theoretical derivation (althought I guess so is any other law ever, Newton's laws of Motion for one. I picked on entropy as it's an constructed concept that has no particular meaning other than to help derive other physical parameters like Temperature through statistics).

The yet to unify defination of entropy might have contributed to the fact that 2nd law still lacks of theoretical defination, and the fact it works well constructing isolated systems that works with experimental data might have fuelled the thought that 2nd law is universal. 

The one proposed prove of the 2nd law is through Boltzmann's "H" theorem. The "H" theorem derives that Entropy always increase with time from supposively the Newton's law of motion F=ma. There are several things that doesn't quite work. First one is the "Loschmidt's paradox" where F-ma is time reversal symmetrical, which means if you change the direction of time(t = -t) the direction of x doesn't change (x=x). This means if Entropy increase forward in time, entropy also have to increase backward in time. The second point is that although Newton's law seemingly a solid foundation, it makes much assumption such as it assumes the force field is space symmetrical(I do realise this concern is a little bit stretched. There are many reason to believe all force fields are symmetrical. One consequence of force not being symmetrical is that energy conservation would be broken, and almost all physics we have would be in doubt.) Also Newton's law itself is an empirical law, in fact, we know it's only an estimate.

Anyway, the 2nd law might be justified through a statistical point of view such that, a system has the largest probability to fall into the configuration that has most statistical weight over time (very complicated yet so obvious, of course a system is most likely to be in the state that it's most likely to be in!). But with this defination the 2nd law merely becomes a "likelyhood" rather than a law. And while the system is most likely to be found in a equilibrium given enough time (the most likely state), there's also chances that we find it in some lower entropy configurations, no matter how unlikely it may be.

And this might bring me to share my thoughts on heat death of the universe. I have no background in astrophysics, not very good at special relativity and has no education in GR. I merely want to offer a statistical (maybe a little bit mechanics) point of view. I understand that the canonical systems we build is not quite applicable to the universe where long range force (gravity) plays a dominant role, and these forces can't be accounted for by isolated systems (the systems inevitably interact and becomes not extensive) but notheless I believe the statistical configurations would be applicable as stat seems to be universal (well the stats we know has already been broken by Bose, through indistinguishable particles, so there's no reason to believe it won't be broken again).

If entropy is to be taken statistically that, a system is most lilkely to end up in a most probable configuration, there's no reason not to believe sometimes it ends up in a less probable configuration. The chances might be astronomically small, but the universe is astronomically large (again I have no idea about the size I'm dealing with here) so there's that. 

Following this, I may suggest that we happens to live in a local non-equilibrium fluctuation of a largely equilibrium universe. Although from my sorry understanding of astrophysics, the universe is not quite in equilibrium, so there's that.