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Entropy 2013, 15(12), 5580-5596; doi:10.3390/e15125580

A Characterization of Conserved Quantities in Non-Equilibrium Thermodynamics

E.T.S. Ingenieros Industriales, Technical University of Madrid, Madrid 28006, Spain
Received: 30 August 2013 / Revised: 15 November 2013 / Accepted: 6 December 2013 / Published: 17 December 2013
(This article belongs to the Special Issue Advances in Methods and Foundations of Non-Equilibrium Thermodynamics)
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Abstract

The well-known Noether theorem in Lagrangian and Hamiltonian mechanics associates symmetries in the evolution equations of a mechanical system with conserved quantities. In this work, we extend this classical idea to problems of non-equilibrium thermodynamics formulated within the GENERIC (General Equations for Non-Equilibrium Reversible-Irreversible Coupling) framework. The geometric meaning of symmetry is reviewed in this formal setting and then utilized to identify possible conserved quantities and the conditions that guarantee their strict conservation. Examples are provided that demonstrate the validity of the proposed definition in the context of finite and infinite dimensional thermoelastic problems.
Keywords: non-equilibrium thermodynamics; symmetry; Noether’s theorem; conserved quantities non-equilibrium thermodynamics; symmetry; Noether’s theorem; conserved quantities
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Romero, I. A Characterization of Conserved Quantities in Non-Equilibrium Thermodynamics. Entropy 2013, 15, 5580-5596.

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