On the possible distributions of temperature in nonequilibrium steady states

Abstract

Superstatistics is a framework in nonequilibrium statistical mechanics that successfully describes a wide variety of complex systems, including hydrodynamic turbulence, weakly-collisional plasmas, cosmic rays, power grid fluctuations, among several others. In this work we analyze the class of nonequilibrium steady-state systems consisting of a subsystem and its environment, and where the subsystem is described by the superstatistical framework. In this case we provide an answer to the mechanism by which a broad distribution of temperature arises, namely due to correlation between subsystem and environment. We prove that there is a unique microscopic definition of inverse temperature compatible with superstatistics, in the sense that all moments of and coincide. The function however, cannot depend on the degrees of freedom of the system itself, only on the environment, in full agreement with our previous impossibility theorem (Davis and Gutiérrez 2018 Physica A 505 864–70). The present results also constrain the possible joint ensembles of system and environment compatible with superstatistics.