Entropy Production in Collisionless Systems. I. Large Phase-Space Occupation Numbers

TL;DR

This paper explores how entropy production rates influence the stationary states of collisionless self-gravitating systems, proposing new theoretical expressions and conditions for extremizing entropy production.

Contribution

It introduces novel formulations for entropy production in collisionless systems and derives conditions for extremizing entropy production rates, advancing the thermodynamic understanding of such systems.

Findings

Derived expressions for entropy production rate in self-gravitating systems

Identified conditions for extremizing entropy production rate

Discussed implications of relaxation functions in collisionless relaxation

Abstract

Certain thermal non-equilibrium situations, outside of the astrophysical realm, suggest that entropy production extrema, instead of entropy extrema, are related to stationary states. In an effort to better understand the evolution of collisionless self-gravitating systems, we investigate the role of entropy production and develop expressions for the entropy production rate in two particular statistical families that describe self-gravitating systems. From these entropy production descriptions, we derive the requirements for extremizing the entropy production rate in terms of specific forms for the relaxation function in the Boltzmann equation. We discuss some implications of these relaxation functions and point to future work that will further test this novel thermodynamic viewpoint of collisionless relaxation.