Understanding Non-equilibrium Thermodynamics

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

“…This is in accordance with the experimental evidence that the local-equilibrium temperature loses its validity in situations where the deviation from equilibrium ensemble is not negligible, as for example the heat propagation in nanosystems [22,30,36,[39][40][41].…”

“…Extensions of Eq. (1) to the nonlinear regime may be obtained in the framework of Extended Irreversible Thermodynamics (EIT) [6,7,21,27,28], a theory which upgrades the dissipative fluxes to the rank of independent thermodynamic variables [10,22,[29][30][31], while nonlinear generalizations of Eq. (2) have been obtained either in EIT [5], or in the framework of the thermomass theory [12][13][14], which also pays a special attention to nonlinear terms in the heat transport equation.…”

“…This represents a nonlinear evolution equation for the heat flux which allows to consider in a simple way some nonlocal, nonlinear and memory effects, beside to study the propagation of heat waves, which is a well-known topic in current nonequilibrium thermodynamics [22,30,[46][47][48].…”

A hierarchy of hydrodynamic models for silicon carbide semiconductors

“…In this context, in order to introduce the thermodynamic forces, one must invoke the Local Equilibrium Hypothesis [7] (and consequently the Gibbs relation), which we have not introduced in our theory.…”

“…For engineering purposes, one has to introduce hydrodynamic models, which are obtained by taking the moments of the BBP equations and by using a suitable truncation procedure. This problem can be solved with the help of the variational method known as Maximum Entropy Principle (MEP) [7,8], which allows the determination of the nonequilibrium distribution function, and consequently, of the constitutive relations. Recently, this methodology as been applied to SiC [9] obtaining a closed set of balance equation of hyperbolic-type.…”