Temperature in nonequilibrium states and non-Fourier heat conduction

Abstract

Macroscopic models beyond Fourier's law for fast-transient heating and heat transport in nanosystems have been proposed. Consequently, some basic quantities such as entropy and temperature need to be modified. From the viewpoint of the thermomass theory, we show that in nonequilibrium systems where heat conduction occurs, the static pressure of thermomass is lower than the total pressure, corresponding to a nonequilibrium temperature lower than the local-equilibrium temperature. The definition of entropy is also modified since the phonon kinetic energy conserves the ability to do work. The nonequilibrium temperature based on the thermomass theory is close to that in the extended irreversible thermodynamics. The microscopic foundation is explored through a phonon Boltzmann derivation. The higher-order contributions to the distribution function are found to be responsible for such modification of temperature. Therefore, the thermomass model gives not only non-Fourier conduction law, but also a physical picture about modified state variables in nonequilibrium states.