Comparison of some geometric frameworks for dissipative evolution in multiscale non-equilibrium thermodynamics

TL;DR

This paper reviews and compares various geometric frameworks for modeling dissipation in multiscale non-equilibrium thermodynamics, highlighting their relationships and differences.

Contribution

It provides a comprehensive comparison of classical, gradient, Rayleigh, dissipative d'Alembert, and Poisson bracket frameworks for dissipative evolution.

Findings

Rayleigh dissipation potential relates to gradient dynamics.

Dissipative d'Alembert framework connects with classical thermodynamics.

Poisson brackets generate dissipative evolution in certain frameworks.

Abstract

In this paper, we review and compare some geometric frameworks for dissipation in non-equilibrium thermodynamics. We start with a brief overview of classical irreversible thermodynamics and gradient dynamics. Then we discuss several specific frameworks including Rayleigh dissipation potential and the dissipative d'Alembert framework, showing their relations with gradient dynamics. Finally, we discuss frameworks for dissipative evolution generated from Poisson brackets.