Boltzmann-Equation Based Derivation of Balance Laws in Irreversible Thermodynamics

TL;DR

This paper introduces a new method for deriving macroscopic balance and constitutive equations in irreversible thermodynamics using Boltzmann equation principles, integrating EIT and GENERIC formalisms.

Contribution

It presents a systematic approach combining thermodynamic principles with Boltzmann equation-based hierarchies for modeling irreversible phenomena.

Findings

Establishes a correspondence with Levermore's moment closure hierarchies.

Provides a microscopic foundation for macroscopic thermodynamic models.

Offers a unified framework integrating EIT and GENERIC formalisms.

Abstract

In this paper we propose a novel approach to construct macroscopic balance equations and constitutive equations describing various irreversible phenomena. It is based on the general principles of non-equilibrium thermodynamics and consists of four basic steps: picking suitable state variables, choosing a strictly concave entropy function, separating entropy fluxes and production rates properly, and determining a dissipation matrix. Our approach takes the advantage of both EIT and GENERIC formalisms, and shows a direct correspondence with Levermore's moment closure hierarchies for the Boltzmann equation. This result may put various macroscopic modeling approaches starting from the general principles of non-equilibrium thermodynamics on a solid microscopic foundation based on the Boltzmann equation.