Superstatistics: Theory and Applications

Abstract

Superstatistics is a superposition of two different statistics relevant for driven nonequilibrium systems with a stationary state and intensive parameter fluctuations. It contains Tsallis statistics as a special case. After briefly summarizing some of the theoretical aspects, we describe recent applications of this concept to three different physical problems, namely a) fully developed hydrodynamic turbulence b) pattern formation in thermal convection states and c) the statistics of cosmic rays.

16 pages, 5 figures. Submitted to Continuum Mechanics and Thermodynamics as a contribution to the topical issue on nonextensive statistical mechanics

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• Fluctuating temperature and baryon chemical potential in heavy-ion collisions and the position of the critical end point in the effective QCD phase diagram
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• Event shape and Multiplicity dependence of Freeze-out Scenario and System Thermodynamics in Proton+Proton Collisions at $\sqrt{s}$ = 13 TeV using PYTHIA8
• Non-extensive entropy from incomplete knowledge of Shannon entropy?
• Generalized thermodynamic uncertainty relations
• Estimation in a fluctuating medium and power-law distributions
• Fluctuating temperature outside superstatistics: thermodynamics of small systems
• Fisher information and thermodynamics' 1st. law
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• Generalized Thermostatistics and Bose-Einstein Condensation
• Kappa distribution from particle correlations in non-equilibrium, steady-state plasmas
• Superstatistics and the quest of generalized ensembles equivalence in a system with long-range interactions
• Zubarev nonequilibrium statistical operator method in Renyi statistics. Reaction-diffusion processes
• Volume effects on the QCD critical end point from thermal fluctuations within the super statistics framework
• On the possible distributions of temperature in nonequilibrium steady states
• Comprehensive Analysis of Market Conditions in the Foreign Exchange Market: Fluctuation Scaling and Variance-Covariance Matrix
• Computational Statistical Mechanics of a confined, three-dimensional Coulomb gas
• A general statistical model for waiting times until collapse of a system
• A superstatistics approach to the modelling of memristor current-voltage responses
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• Chiral phase transition within the linear sigma model in the Tsallis nonextensive statistics based on density operator
• Testing the Isotropic Cauchy Hypothesis
• Superstatistics as the thermodynamic limit of driven classical systems
• Fundamental temperature exclusively determines the validity of superstatistics
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• Temperature fluctuations in finite systems: Application to the one-dimensional Ising chain
• A classification of nonequilibrium steady states based on temperature correlations
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