Thermodynamically consistent generalized hydrodynamic theory of thermal conduction and integral equations of thermal conductivity of simple fluids in electromagnetic fields

Abstract

We have reviewed thermodynamically consistent evolution equations of fluids in an invited review article in the McGill University bicentennial memorial issue [B. C. Eu, Can. J. Chem. (in press) (2021)]. In this article, we apply the generalized hydrodynamic evolution equations of heat fluxes to derive integral equations for thermal conductivity coefficients of fluids in electromagnetic fields, which generalize the linear response theory formula of Green and Kubo to nonlinear heat conduction phenomena. The constitutive equation for the temperature field derived is compared with the temperature evolution equation obtained by Guo et al. [Physica D 342, 24 (2017)] on the basis of extended irreversible thermodynamics. They are considerably different.