TY - JOUR
T1 - From Lagrangian mechanics to nonequilibrium thermodynamics
T2 - A variational perspective
AU - Gay-Balmaz, François
AU - Yoshimura, Hiroaki
N1 - Funding Information:
Funding: F.G.-B. is partially supported by the ANR project GEOMFLUID, ANR-14-CE23-0002-01; H.Y. is partially supported by JSPS Grant-in-Aid for Scientific Research (16KT0024, 24224004), the MEXT “Top Global University Project” and Waseda University (SR 2018K-195).
Publisher Copyright:
© 2019 by the authors.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - 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.
AB - 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.
KW - Continuum thermodynamic systems
KW - Discrete thermodynamic systems
KW - Irreversible processes
KW - Nonequilibrium thermodynamics
KW - Nonholonomic constraints
KW - Variational formulation
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U2 - 10.3390/e21010008
DO - 10.3390/e21010008
M3 - Review article
AN - SCOPUS:85060375785
SN - 1099-4300
VL - 21
JO - Entropy
JF - Entropy
IS - 1
M1 - 8
ER -