Physical variational principle in dissipative media

Abstract

The physical variational principle (PVP) is a physical principle which is implied in the thermodynamic laws. For a conservative system, the PVP is implied in the first thermodynamic law and gives the motion equation. But for a dissipative system, PVP is implied in the extended Gibbs equation, which is the result of the first and second thermodynamic laws. The precision of the PVP in a dissipative system is in the same order of the Gibbs equation. The dissipative work and its converted internal irreversible heat are simultaneously included in the PVP to get the governing equation and the boundary condition of the dissipated variables. The “generalized motion equations” including governing equations of the mechanical momentum and thermoelastic, thermal viscoelastic, thermal elastoplastic, linear thermoelastic diffusive and linear electromagnetic thermoelastic materials etc. can be derived by the PVP of dissipative media in this paper. The conservative system is the special case of the dissipative system. Other than the mathematical variational principle, which is obtained by a known governing equation, the PVP is used to deduce the governing equation. The PVPs including the hyperbolic temperature wave equation with a finite phase speed are also discussed shortly.