Emergence of Tsallis statistics as a consequence of invariance

Abstract

For non-equilibrium systems in a steady state we present two necessary and sufficient conditions for the emergence of $q$-canonical ensembles, also known as Tsallis statistics. These conditions are invariance requirements over the definition of subsystem and environment, and over the joint rescaling of temperature and energy. Our approach is independent of, but complementary to, the notions of Tsallis non-extensive statistics and Superstatistics.

References in corpus (2)

• Wigner Functions for the Pair Angle and Orbital Angular Momentum
• Temperature is not an observable in superstatistics

Cited by in corpus (6)

• Fluctuating temperature outside superstatistics: thermodynamics of small systems
• Kappa distribution from particle correlations in non-equilibrium, steady-state plasmas
• On the possible distributions of temperature in nonequilibrium steady states
• Fundamental temperature exclusively determines the validity of superstatistics
• Fluctuation theorems in nonextensive statistics
• A classification of nonequilibrium steady states based on temperature correlations