Thermodynamic hierarchies of evolution equations

TL;DR

This paper explores the hierarchical structure of evolution equations in non-equilibrium thermodynamics, illustrating how internal variables organize complex physical phenomena across different theories.

Contribution

It introduces a unified hierarchical framework for evolution equations in thermodynamics, encompassing rheology, continuum mechanics, and heat conduction.

Findings

Hierarchical organization of linear constitutive equations in rheology

Hierarchical wave equations in generalized continua

Hierarchical Fourier equations with current multipliers

Abstract

Non-equilibrium thermodynamics with internal variables introduces a natural hierarchical arrangement of evolution equations. Three examples are shown: a hierarchy of linear constitutive equations in thermodynamic rhelogy with a single internal variable, a hierarchy of wave equations in the theory of generalized continua with dual internal variables and a hierarchical arrangement of the Fourier equation in the theory of heat conduction with current multipliers.