Relationships between rational extended thermodynamics and extended irreversible thermodynamics

Abstract

<jats:p>We consider a few conceptual questions on extended thermodynamics, with the aim to contribute to a higher contact between rational extended thermodynamics and extended irreversible thermodynamics. Both theories take a number of fluxes as independent variables, but they differ in the formalism being used to deal with the exploitation of the second principle (rational thermodynamics in the first one and classical irreversible thermodynamics in the second one). Rational extended thermodynamics is more restricted in the range of systems to be analysed, but it is able to obtain a wider number of restrictions and deeper specifications from the second law. By contrast, extended irreversible thermodynamics is more phenomenological, its mathematical formalism is more elementary, but it may deal with a wider diversity of systems although with less detail. Further comparison and dialogue between both branches of extended thermodynamics would be useful for a fuller deployment and deepening of extended thermodynamics. Besides these two approaches, one should also consider the Hamiltonian approach, formalisms with internal variables, and more microscopic approaches, based on kinetic theory or on non-equilibrium ensemble formalisms.</jats:p> <jats:p>This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.</jats:p>

Retracted: Local pressure for inhomogeneous fluids

“…The grand potential associated with the local equilibrium ensemble provides the “equation of state” for generating conjugate variables such as temperature and activity, and is the direct analog of equilibrium thermodynamics. To further clarify the context it is noted that the current work does not relate to the general fields of “nonequilibrium thermodynamics” 18 or “extended thermodynamics.” 19 The former is an attempt to discover universal fundamental principles, similar to those of equilibrium thermodynamics (e.g., a generalized second law, entropy), to govern the dissipative dynamics of macroscopic properties. Extended irreversible thermodynamics takes as the macroscopic fields the usual local conserved fields plus the dissipative fluxes of energy and momentum.…”

Nonequilibrium thermodynamics: emergent and fundamental

“…The compatibility with a statistical treatment, based on a given microscopic or mesoscopic material composition, is a clear benchmark of any general phenomenology and appears here in the papers [1,10,12]. In particular, the compatibility with the kinetic theory is important in [8,6,7,3]. However, nonequilibrium thermodynamics is not necessarily emergent, from the fundamental point of view the compatibility with any nondissipative, ideal theory is expected.…”

Nonlocal and nonlinear effects in hyperbolic heat transfer in a two-temperature model

“…(1). To this aim, we put ourselves in the context of extended thermodynamics [4,15,21,24,25] and assume the following state space:…”