Abstract
In this work, we make a further step in bringing together different approaches to non-equilibrium thermodynamics. The structure of the moment hierarchy derived from the Boltzmann equation is at the heart of rational extended thermodynamics (RET, developed by Ingo Müller and Tommaso Ruggeri). Whereas the full moment hierarchy has the structure expressed in the general equation for the nonequilibrium reversible–irreversible coup- ling (GENERIC), the Poisson bracket structure of reversible dynamics postulated in that approach is a major obstacle for truncating moment hierarchies, which seems to work only in exceptional cases (most importantly, for the five moments associated with conservation laws). The practical importance of truncated moment hierarchies in rarefied gas dynamics and microfluidics motivates us to develop a new strategy for establishing the full GENERIC structure of truncated moment equations, based on non-entropy-producing irreversible processes associated with Casimir symmetry. Detailed results are given for the special case of 10 moments.This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.
Highlights
The purpose of nonequilibrium thermodynamics is to recognize ‘good’ equations
The purpose of this paper is to investigate the relationship between rational extended thermodynamics (RET) and the general equation for the nonequilibrium reversible–irreversible coupling (GENERIC)
We have demonstrated that RET is a special case of GENERIC for the special choice of variables inspired by the moment equations obtained from the Boltzmann equation for rarefied gases
Summary
The purpose of nonequilibrium thermodynamics is to recognize ‘good’ equations. From a physical perspective, this means that thermodynamically admissible evolution equations should guarantee proper balance equations for energy and entropy. We here restrict ourselves to thermodynamic frameworks based on differential evolution equations for extended lists of variables (rather than memory functionals). Finding a list of variables that allows us to formulate an autonomous set of evolution equations is a challenging first step in any application of nonequilibrium thermodynamics. This step should be appreciated as an expression of deep insight, not as an annoying closure problem [7]. Convection conserves entropy, and guaranteeing the non-negativity of entropy production by irreversible processes is a central element of any framework of nonequilibrium thermodynamics. A detailed comparison with a version of rational thermodynamics [21], in which Liu’s procedure [22] for guaranteeing the non-negativity of entropy production is used, has been made in the context of a simple discrete system [23]
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