TY - JOUR
T1 - A Lagrangian variational formulation for nonequilibrium thermodynamics. Part II
T2 - Continuum systems
AU - Gay-Balmaz, François
AU - Yoshimura, Hiroaki
N1 - Funding Information:
The authors thank C. Gruber for extremely helpful discussions. 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 26400408 , Grant-in-Aid for Scientific Research 16KT0024 ), JST (CREST) , Waseda University ( SR 2014B-162 , SR 2015B-183 ), the IRSES project “Geomech” ( 246981 ) within the 7th European Community Framework Programme, and the MEXT “Top Global University Project” at Waseda University .
Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2017/1/1
Y1 - 2017/1/1
N2 - Part I of this paper introduced a Lagrangian variational formulation for nonequilibrium thermodynamics of discrete systems. This variational formulation extends Hamilton's principle to allow the inclusion of irreversible processes in the dynamics. The irreversibility is encoded into a nonlinear nonholonomic constraint given by the expression of entropy production associated to all the irreversible processes involved. In Part II, we develop this formulation for the case of continuum systems by extending the setting of Part I to infinite dimensional nonholonomic Lagrangian systems. The variational formulation is naturally expressed in the material representation, while its spatial version is obtained via a nonholonomic Lagrangian reduction by symmetry. The theory is illustrated with the examples of a viscous heat conducting fluid and its multicomponent extension including chemical reactions and mass transfer.
AB - Part I of this paper introduced a Lagrangian variational formulation for nonequilibrium thermodynamics of discrete systems. This variational formulation extends Hamilton's principle to allow the inclusion of irreversible processes in the dynamics. The irreversibility is encoded into a nonlinear nonholonomic constraint given by the expression of entropy production associated to all the irreversible processes involved. In Part II, we develop this formulation for the case of continuum systems by extending the setting of Part I to infinite dimensional nonholonomic Lagrangian systems. The variational formulation is naturally expressed in the material representation, while its spatial version is obtained via a nonholonomic Lagrangian reduction by symmetry. The theory is illustrated with the examples of a viscous heat conducting fluid and its multicomponent extension including chemical reactions and mass transfer.
KW - Continuum systems
KW - Irreversible processes
KW - Lagrangian formulation
KW - Nonequilibrium thermodynamics
KW - Nonholonomic constraints
KW - Variational formulation
UR - http://www.scopus.com/inward/record.url?scp=84998780433&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84998780433&partnerID=8YFLogxK
U2 - 10.1016/j.geomphys.2016.08.019
DO - 10.1016/j.geomphys.2016.08.019
M3 - Article
AN - SCOPUS:84998780433
SN - 0393-0440
VL - 111
SP - 194
EP - 212
JO - Journal of Geometry and Physics
JF - Journal of Geometry and Physics
ER -