The second law, maximum entropy production and Liouville's theorem

TL;DR

This paper extends Jaynes' proof of the second law to show that Liouville's theorem implies maximum entropy production in open, non-equilibrium systems, linking fundamental physics principles to stationary state selection.

Contribution

It demonstrates that Liouville's theorem implies maximum entropy production for stationary states of open systems, extending Jaynes' proof to non-equilibrium thermodynamics.

Findings

Liouville's theorem implies MaxEP in open systems.

MaxEP states are more adaptable to environmental variations.

Connection between phase volume invariance and fluctuation theorem.

Abstract

In 1965 Jaynes provided an intuitively simple proof of the 2nd law of thermodynamics as a general requirement for any macroscopic transition to be experimentally reproducible. His proof was based on Boltzmann's formula S = klnW and the dynamical invariance of the phase volume W for isolated systems (Liouville's theorem). Here Jaynes' proof is extended to show that Liouville's theorem also implies maximum entropy production (MaxEP) for the stationary states of open, non-equilibrium systems. According to this proof, MaxEP stationary states are selected because they can exist within a greater number of environments than any other stationary states. Liouville's theorem applied to isolated systems also gives an intuitive derivation of the fluctuation theorem in a form consistent with an earlier conjecture by Jaynes on the probability of violations of the 2nd law. The present proof of MaxEP, while largely heuristic, suggests an approach to establishing a more fundamental basis for MaxEP using Jaynes' maximum entropy formulation of statistical mechanics.