About the maximum entropy principle in non equilibrium statistical mechanics

TL;DR

The paper critically examines the maximum entropy principle in non-equilibrium statistical mechanics, demonstrating its limitations and arguing that traditional dynamic analysis is necessary for accurate predictions in non-equilibrium systems.

Contribution

The paper provides a detailed critique of the maximum entropy principle's applicability to non-equilibrium systems, highlighting its failures and emphasizing the importance of traditional dynamic methods.

Findings

MEP leads to incorrect predictions in non-equilibrium cases

Traditional methods outperform MEP in non-equilibrium scenarios

Success of MEP in equilibrium is due to specific physical conditions

Abstract

The maximum entropy principle (MEP) apparently allows us to derive, or justify, fundamental results of equilibrium statistical mechanics. Because of this, a school of thought considers the MEP as a powerful and elegant way to make predictions in physics and other disciplines, which constitutes an alternative and more general method than the traditional ones of statistical mechanics. Actually, careful inspection shows that such a success is due to a series of fortunate facts that characterize the physics of equilibrium systems, but which are absent in situations not described by Hamiltonian dynamics, or generically in nonequilibrium phenomena. Here we discuss several important examples in non equilibrium statistical mechanics, in which the MEP leads to incorrect predictions, proving that it does not have a predictive nature. We conclude that, in these paradigmatic examples, the "traditional" methods based on a detailed analysis of the relevant dynamics cannot be avoided.