Thermodynamics with Internal Variables. Part I. General Concepts

Advances in Thermodynamics of Ferroelectric Phase Transitions

“…In order to get the more adequate approaches, we should pay attention to the new developments of non-equilibrium thermodynamics. The thermodynamics with internal variables [25] and the extended ( irreversible ) thermodynamics [26] are two current ones. They all expand the fundamental variables spaces to describe the irreversible processes more adequately.…”

Generalized Hamilton’s Principle for Inelastic Bodies Within Non-Equilibrium Thermodynamics

“…It follows that the existence of a free-energy density can be assumed from which the entropy density and the stress can be derived. Some detailed and overall results on internal variable and constrained equilibrium state have been obtained by Kestin and Rice [17], Germain, Nguyen and Suquet [18], Maugin and Muschik [19], Chaboche [20,21] and Yang et al [22,23] and others.…”

Entropy Principle and Recent Results in Non-Equilibrium Theories

“…This is the case in the inelastic behavior of solids or in the relaxation effects in thermo-viscous fluids [123,124]. These non-equilibrium parameters, whose nature depends on the phenomenon at hand, are introduced through ordinary differential equations, called kinetic equations, on the basis of physical experiments.…”

“…In such a case the balance equations are difficult to solve, and sometime the well posedness of the relevant Cauchy problem is not guaranteed [146]. Another possibility, used both in RT [147][148][149] and in CIT [150] is to introduce internal state variables [123,126]. Such an approach leads to more simple systems of equations.…”