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A Rather General Variational Principle for Purely Dissipative Non‐Stationary Processes
Author(s) -
Lambermont J.,
Lebon G.
Publication year - 1972
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19724830104
Subject(s) - variational principle , dissipative system , stationary state , physics , thermal conduction , isotropy , entropy production , classical mechanics , reciprocal , mathematical analysis , thermodynamics , mathematics , quantum mechanics , linguistics , philosophy
A general variational principle concerning non‐stationary purely dissipative phenomena, obeying O NSAGER 's reciprocal relations, is presented. The principle expresses that the variation of the sum of the total entropy production and the time derivative of the M ASSIEU function is equal to zero. It is shown that the E ULER ‐L AGRANGE equations corresponding to arbitrary variations of the state variables yield the conservation laws. Other general criteria for non‐stationary processes have been given by G LANSDORFF ‐P RIGOGINE and G YARMATI . They are compared with our principle. Two illustrative examples are considered: coupled heat and electrical conduction in an isotropic medium and chemical reactions coupled with diffusion of matter and heat conduction in a multi‐component fluid.