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 $\mathcal{B}$ of inverse temperature compatible with superstatistics, in the sense that all moments of $\mathcal{B}$ and $\beta =1/(k_{B}T)$ coincide. The function $\mathcal{B}$ however, cannot depend on the degrees of freedom of the system itself, only on the environment, in full agreement with our previous impossibility theorem [Physica A \textbf{505}, 864-870 (2018)]. The present results also constrain the possible joint ensembles of system and environment compatible with superstatistics.

References in corpus (22)

• Superstatistics
• Non Linear Kinetics underlying Generalized Statistics
• A Dynamical Approach to Temperature
• Non-Gaussian power grid frequency fluctuations characterized by Lévy-stable laws and superstatistics
• From time series to superstatistics
• Generalized entropies and the transformation group of superstatistics
• Superstatistics: Theory and Applications
• Statistics of 3-dimensional Lagrangian turbulence
• Modelling train delays with q-exponential functions
• Intensity Thresholds and the Statistics of the Temporal Occurrence of Solar Flares
• Thermodynamic Derivation of the Tsallis and Rényi Entropy Formulas and the Temperature of Quark-Gluon Plasma
• Generalized statistical mechanics for superstatistical systems
• Bayesian approach to superstatistics
• Finite Bath Fluctuation Theorem
• Single-particle velocity distributions of collisionless, steady-state plasmas must follow Superstatistics
• A maximum entropy thermodynamics of small systems
• Special Relativity induced by Granular Space
• Temperature is not an observable in superstatistics
• An additive variant of Tsallis generalized entropy
• Emergence of Tsallis statistics as a consequence of invariance
• Superstatistics and temperature fluctuations
• Superstatistics and the quest of generalized ensembles equivalence in a system with long-range interactions

Cited by in corpus (5)

• Fluctuating temperature outside superstatistics: thermodynamics of small systems
• Kappa distribution from particle correlations in non-equilibrium, steady-state plasmas
• A superstatistical measure of distance from canonical equilibrium
• Conditional maximum entropy and Superstatistics
• A classification of nonequilibrium steady states based on temperature correlations