Nonequilibrium thermodynamics: emergent and fundamental

Abstract

<jats:p>How can we derive the evolution equations of dissipative systems? What is the relation between the different approaches? How much do we understand the fundamental aspects of a second law based framework? Is there a hierarchy of dissipative and ideal theories at all? How far can we reach with the new methods of nonequilibrium thermodynamics?</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

“…Since the equilibrium ensemble is stationary, the equilibrium average of Equation (18) gives the stationary equilibrium force balance equation…”

“…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.…”

Coexisting Ordered States, Local Equilibrium-like Domains, and Broken Ergodicity in a Non-turbulent Rayleigh-Bénard Convection at Steady-state

“…Although far-from-equilibrium systems are ubiquitous in nature, a serious thermodynamic treatment of their behavior remains largely an uncharted territory [2,9,10,5,11,12,13,14,15]. One of the several ways to extend equilibrium thermodynamics to out-of-equilibrium systems is through the assumption of local equilibrium in classical irreversible systems [16,17].…”

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), that 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.…”