Recent Advances in Conservation-Dissipation Formalism for Irreversible Processes

TL;DR

This review summarizes recent progress in the Conservation-Dissipation Formalism (CDF), a framework for developing thermodynamically consistent and mathematically stable models for various irreversible processes across multiple scientific fields.

Contribution

It introduces the physical motivations, mathematical foundations, and diverse applications of CDF, highlighting its ability to unify and extend existing models in non-equilibrium thermodynamics.

Findings

CDF provides a systematic way to construct stable models for irreversible processes.

Applications include non-Fourier heat conduction, non-Newtonian fluids, and wave propagation.

Connections with other thermodynamic theories are also discussed.

Abstract

The main purpose of this review is to summarize the recent advances of the Conservation-Dissipation Formalism (CDF), a new way for constructing both thermodynamically compatible and mathematically stable and well-posed models for irreversible processes. The contents include but are not restricted to the CDF's physical motivations, mathematical foundations, formulations of several classical models in mathematical physics from master equations and Fokker-Planck equations to Boltzmann equations and quasi-linear Maxwell equations, as well as novel applications in the fields of non-Fourier heat conduction, non-Newtonian viscoelastic fluids, wave propagation/transportation in geophysics and neural science, soft matter physics, \textit{etc.} Connections with other popular theories in the field of non-equilibrium thermodynamics are examined too.