Entropy Principle and Recent Results in Non-Equilibrium Theories

Abstract

We present the state of the art on the modern mathematical methods of exploiting the entropy principle in thermomechanics of continuous media. A survey of recent results and conceptual discussions of this topic in some well-known non-equilibrium theories (Classical irreversible thermodynamics CIT, Rational thermodynamics RT, Thermodynamics of irreversible processes TIP, Extended irreversible thermodynamics EIT, Rational Extended thermodynamics RET) is also summarized.

Theories and heat pulse experiments of non-Fourier heat conduction

“…in (5)-(7) the number of parameters is higher [8,46,47]. In RET the microstructure is unavoidable in EIT the microstructure is flexible.…”

“…Remarkably one needs only three parameters here, the Debye speed and the R and N process related relaxation times [6,9,46].…”

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

“…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.…”

“…Indeed, if generalized heat transport equations are used, it turns out that the analysis of their consistency with the second law of thermodynamics requires a generalized framework, where the entropy and the entropy flux are not known a priori. In fact, entropy and entropy flux are found to be, already in simple situations, more general than their local-equilibrium forms [9][10][11].…”

The role of several heat transfer mechanisms on the enhancement of thermal conductivity in nanofluids

“…Here, we follow the line of thought of extended irreversible thermodynamics (EIT) [30][31][32][33], which is a non-equilibrium thermodynamics theory especially suited to treat small-scale effects. The main idea underlying EIT is to upgrade the thermodynamic fluxes, like the heat flux to the status of independent variable at the same level as the classical variable, the temperature.…”