No Mathematical Proof of the 2nd Law of Thermodynamics

ChatGPT informs me that there is no mathematical proof of 2nd Law of thermodynamics and so it is simply an empirical law albeit:

• supported by a wealth of empirical evidence
• deeply ingrained in our understanding of how physical systems behave
• while mathematical frameworks like statistical mechanics provide a basis for explaining the law, the principle itself is derived from the consistency of these explanations with real-world observations.

ChatGPT is useful in the sense that it reports what it has learned from physics literature, while it is not intelligent enough to cover up like a real theoretical physicist, who would never admit anything like that.

In any case we learn that that there is no mathematical proof/explanation of the 2nd Law. 

It means that this could be added to the list of Clay Millennium Problems, or even better replace the closely related Navier-Stokes problem, which is still open without any progress to a solution, see previous post.

What do you think? Is there a mathematical proof? Or not? 

PS Recall that Boltzmann's H-theorem stating a steady progress to a Maxwellian equilibrium in a dilute gas attempted as a mathematical proof of the 2nd Law, is based on Boltzmann's Stosszahlansatz asking two particles about to collide to be uncorrelated as an assumption of statistical nature, which however cannot be verified nor assumed to be true in any generality.