General expression for entropy production in transport processes based on the thermomass model

Abstract

The entropy production in classical irreversible thermodynamics is expressed as a bilinear form of generalized (driving) forces and conjugated (driven) fluxes, which suffers from the arbitrary decomposition of the forces and the fluxes, and the possible negative entropy production in non-Fourier heat conduction problems (heat waves). This paper presents a general form of the entropy production for heat conduction based on the thermomass model, which is the product of the friction force and the drift velocity of the thermomass divided by the temperature; it holds true for both Fourier and non-Fourier heat conduction. Then a generalization of the entropy production is given for other kinds of linear and nonlinear transport processes. The general expression for entropy production is consistent with that given by extended irreversible thermodynamics, where the system entropy depends not only on the classical variables, but also on the dissipative fluxes, for example, the heat flux in heat conduction problems.

Heat-pulse propagation along nonequilibrium nanowires in thermomass theory

“…In the present paper we analyzed the consequences predicted by the TM theory [16][17][18] on the speed of propagation of heat waves. In the special case of a silicon nanowire submitted to a linear temperature gradient, we pointed out the very important role that nonlinear effects may have in practical applications.…”

“…However, the temperature dependence of φ in Eqs. (18) points out that also in this formalism both propagation speeds are temperature dependent, implying that the two boundaries of a energy pulse move with slightly different speeds. We note that the consequences of accounting for Eq.…”

“…Among the different theoretical approaches describing heat transport beyond the Fourier law, the thermomass (TM) theory [16][17][18] represents a recent proposal which is growing in interest. In this theory, whose thermodynamic compatibility with second law has been analyzed in Ref.…”

Constitutive equations for heat conduction in nanosystems and nonequilibrium processes: an overview

“…This collection is made by quasiparticles of heat carriers, called thermons, which are representative of the vibrations of the molecules generated by heating the conductor and whose mass may be calculated from the Einstein's mass-energy duality. For crystals, the thermomass gas is just the phonon gas, for pure metals it will be attached on the electron gas, and for semi-metals it will be constituted by both these different gases [13,[49][50][51].…”

“…The Thermomass (TM) theory [13,[49][50][51] provides a further example of nonlinear heat-transport equation with thermal lag. In TM theory the heat transport is due to the motion of a gas-like collection of heat carriers, characterized by an effective mass density and flowing through the medium due to a thermomass-pressure gradient.…”