Temperature in non-equilibrium states: a review of open problems and current proposals

Abstract

The conceptual problems arising in the definition and measurement of temperature in nonequilibrium states are discussed in this paper in situations where the local-equilibrium hypothesis is no longer satisfactory. This is a necessary and urgent discussion because of the increasing interest in thermodynamic theories beyond local equilibrium, in computer simulations, in non-linear statistical mechanics, in new experiments, and in technological applications of nanoscale systems and material sciences. First, we briefly review the concept of temperature from the perspectives of equilibrium thermodynamics and statistical mechanics. Afterwards, we explore which of the equilibrium concepts may be extrapolated beyond local equilibrium and which of them should be modified, then we review several attempts to define temperature in non-equilibrium situations from macroscopic and microscopic bases. A wide review of proposals is offered on effective non-equilibrium temperatures and their application to ideal and real gases, electromagnetic radiation, nuclear collisions, granular systems, glasses, sheared fluids, amorphous semiconductors and turbulent fluids. The consistency between the different relativistic transformation laws for temperature is discussed in the new light gained from this perspective. A wide bibliography is provided in order to foster further research in this field.

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

“…and depends on the fluxes [3]. 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].…”

“…When the extended entropy (12a) is used instead of the local-equilibrium entropy, the resulting absolute temperature is [3] (13) 1 T = ∂s ∂u = ∂s eq ∂u − ∂ ∂u…”

“…One of them is the meaning of temperature and its relation with heat transport [3][4][5][6][7]. In fact, different degrees of freedom, far from equilibrium, may be associated with different "temperatures".…”

Nonequilibrium phase transitions

“…In the viewpoint of synergetic, Olemskoi and Klepikov [25] describe the spatiotemporal pattern in non-equilibrium systems in a unified way using the concept of order parameter, conjugate field and control parameter. Casas-Vazquez and Jou [26] recently give a comprehensive review about the study of the concept of temperature in non-equilibrium states. To meet the need of computer simulation, new experiments, and study of nanoscale systems, new concepts of temperature in non-equilibrium conditions have been proposed from both macroscopic and microscopic basis [26].…”

“…Casas-Vazquez and Jou [26] recently give a comprehensive review about the study of the concept of temperature in non-equilibrium states. To meet the need of computer simulation, new experiments, and study of nanoscale systems, new concepts of temperature in non-equilibrium conditions have been proposed from both macroscopic and microscopic basis [26].…”