Fundamental temperature exclusively determines the validity of superstatistics

Abstract

The theory of superstatistics is a generalization of Boltzmann-Gibbs statistical mechanics which admits temperature fluctuations, and generates non-canonical ensembles from the distribution function of these fluctuations. Recently, some results have been presented showing that superstatistics is not universally applicable, but several conditions on the so-called fundamental inverse temperature function ${\beta }_F$ must be met by any superstatistical model. In this work we provide a set of neccessary and sufficient conditions for a non-equilibrium steady state model to be expressible by superstatistics, showing that ${\beta }_F$ by itself determines the existence of a superstatistical distribution of temperature.

References in corpus (17)

• Superstatistics
• Non-Gaussian power grid frequency fluctuations characterized by Lévy-stable laws and superstatistics
• Nonextensive statistical mechanics and economics
• Superstatistics: Theory and Applications
• Superstatistical fluctuations in time series: Applications to share-price dynamics and turbulence
• Bayesian approach to superstatistics
• Single-particle velocity distributions of collisionless, steady-state plasmas must follow Superstatistics
• Universality of market superstatistics
• Statistical Mechanics in the Extended Gaussian Ensemble
• Superstatistical modelling of protein diffusion dynamics in bacteria
• Temperature is not an observable in superstatistics
• Applications of the divergence theorem in Bayesian inference and MaxEnt
• Fluctuating temperature outside superstatistics: thermodynamics of small systems
• Emergence of Tsallis statistics as a consequence of invariance
• Superstatistics and temperature fluctuations
• Kappa distribution from particle correlations in non-equilibrium, steady-state plasmas
• Conditional maximum entropy and Superstatistics