The second law of thermodynamics isn't really a fundamental physical law, but rather a promise based on statistics that says "disorder will increase or stay constant in a closed physical system". That said, it's entirely possible for entropy to spontaneously decrease in a closed system, the probability of this happening is just astronomically small for typical macroscopic systems. Example: If you have a system consis…
The second law of thermodynamics is as fundamental as the uncertainty principle: The former is a result from markov chains and information theory, the latter is a result from fourier analysis of conjugate variables. What would you consider a "fundamental physical law"?
I'm surprised that Markov chains would be involved when the laws of physics are deterministic.
The Poincare recurrence theorem has always suggested to me that the second law is not as fundamental as other laws. For a finite system with finite phase space, the state of a system will traverse closed loops, repeating forever with no steady increase or decrease in entropy. (Edit: to be clear, I'm not claiming that what I just described is the Poincare recurrence theorem or that it applies to our universe. But it is worth considering systems where the second law doesn't apply and trying to figure out how and if they differ critically from reality.)
https://en.wikipedia.org/wiki/Poincar%C3%A9_recurrence_theor...
Not that my background is worth anything, but just so you know where I'm coming from, I have a PhD in physics, spent years thinking about the entropy of computation, and wrote parts of the Wikipedia entry on Maxwell's demon. I think much of the disagreement over entropy and the second law comes from how we frame the problem.