Classical and Multiscale Non-equilibrium Thermodynamics

TL;DR

This work compares classical non-equilibrium thermodynamics with multiscale, GENERIC-based approaches to macroscopic systems, showing that classical theory arises as the nondissipative subset of a broader framework that couples Hamiltonian kinematics with gradient dissipation. By expressing time evolution through a Poisson bracket and a dissipation potential, the authors unify diverse mesoscopic theories and elucidate how local equilibrium, energy-entropy relations, and conservation laws interrelate. A key contribution is the demonstration that the Braun-Le Châtelier principle extends to far-from-equilibrium dissipation, illustrated via a two-reaction example within gradient dynamics. The multiscale framework thus provides a principled, geometric basis for analyzing complex fluids and other systems where fast and slow processes interact, with implications for stability, hyperbolicity, and the design of constitutive relations.

Abstract

Classical and multiscale non-equilibrium thermodynamics have different histories and different objectives. In this Note we explain the differences and review some topics in which the multiscale viewpoint of mesoscopic time evolution of macroscopic systems helped to advance the classical non-equilibrium thermodynamics. Eventually, we illustrate the Braun-Le Chatelier principle in dissipative thermodynamics.