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Entropy 2019, 21(1), 8; https://doi.org/10.3390/e21010008

From Lagrangian Mechanics to Nonequilibrium Thermodynamics: A Variational Perspective

1
Centre National de la Recherche Scientifique (CNRS), Le Laboratoire de Météorologie Dynamique (LMD), Ecole Normale Supérieure, 75005 Paris, France
2
School of Science and Engineering, Waseda University, Tokyo 169-8050, Japan
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Received: 21 November 2018 / Revised: 14 December 2018 / Accepted: 16 December 2018 / Published: 23 December 2018
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Abstract

In this paper, we survey our recent results on the variational formulation of nonequilibrium thermodynamics for the finite-dimensional case of discrete systems, as well as for the infinite-dimensional case of continuum systems. Starting with the fundamental variational principle of classical mechanics, namely, Hamilton’s principle, we show, with the help of thermodynamic systems with gradually increasing complexity, how to systematically extend it to include irreversible processes. In the finite dimensional cases, we treat systems experiencing the irreversible processes of mechanical friction, heat, and mass transfer in both the adiabatically closed cases and open cases. On the continuum side, we illustrate our theory using the example of multicomponent Navier–Stokes–Fourier systems. View Full-Text
Keywords: nonequilibrium thermodynamics; variational formulation; nonholonomic constraints; irreversible processes; discrete thermodynamic systems; continuum thermodynamic systems nonequilibrium thermodynamics; variational formulation; nonholonomic constraints; irreversible processes; discrete thermodynamic systems; continuum thermodynamic systems
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Gay-Balmaz, F.; Yoshimura, H. From Lagrangian Mechanics to Nonequilibrium Thermodynamics: A Variational Perspective. Entropy 2019, 21, 8.

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