Maximum entropy change and least action principle for nonequilibrium systems

TL;DR

This paper establishes a connection between maximum path information and the least action principle in nonequilibrium systems, showing that the most probable paths follow least action and relate to entropy change, with implications for chaotic dynamics.

Contribution

It introduces a maximum path information principle that is equivalent to the least action principle for irregular dynamics and derives invariant measures for chaotic systems in fractal phase space.

Findings

Most probable paths follow least action.

Maximum path information relates to entropy change.

Invariant measures for chaotic systems are derived.

Abstract

A path information is defined in connection with different possible paths of irregular dynamic systems moving in its phase space between two points. On the basis of the assumption that the paths are physically differentiated by their actions, we show that the maximum path information leads to a path probability distribution in exponentials of action. This means that the most probable paths are just the paths of least action. This distribution naturally leads to important laws of normal diffusion. A conclusion of this work is that, for probabilistic mechanics or irregular dynamics, the principle of maximization of path information is equivalent to the least action principle for regular dynamics. We also show that an average path information between the initial phase volume and the final phase volume can be related to the entropy change defined with natural invariant measure of dynamic system. Hence the principles of least action and maximum path information suggest the maximum entropy change. This result is used for some chaotic systems evolving in fractal phase space in order to derive their invariant measures.