Superstatistics, thermodynamics, and fluctuations

Abstract

A thermodynamic-like formalism is developed for superstatistical systems based on conditional entropies. This theory takes into account large-scale variations of intensive variables of systems in nonequilibrium stationary states. Ordinary thermodynamics is recovered as a special case of the present theory, and corrections to it can be systematically evaluated. A generalization of Einstein's relation for fluctuations is presented using a maximum entropy condition.

16 pages, no figures. The title changed, some explanations and references added. Accepted for publication in Phys. Rev. E

References in corpus (17)

• Superstatistics
• Interpretation of the nonextensitivity parameter $q$ in some applications of Tsallis statistics and Lévy distributions
• Dynamical foundations of nonextensive statistical mechanics
• From time series to superstatistics
• Constructing a statistical mechanics for Beck-Cohen superstatistics
• Asymptotics of superstatistics
• Defect turbulence and generalized statistical mechanics
• Dynamical model and nonextensive statistical mechanics of a market index on large time windows
• Statistics of 3-dimensional Lagrangian turbulence
• Generalized statistical mechanics of cosmic rays
• Lagrangian acceleration statistics in turbulent flows
• Intensity Thresholds and the Statistics of the Temporal Occurrence of Solar Flares
• Coarse-grained distributions and superstatistics
• Superstatistical generalization of the work fluctuation theorem
• Non-additivity of Tsallis entropies and fluctuations of temperature
• Superstatistics in random matrix theory
• Hierarchical and mixing properties of static complex networks emerging from the fluctuating classical random graphs

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• Generalized statistical mechanics for superstatistical systems
• Superstatistical distributions from a maximum entropy principle
• Intermediate statistics as a consequence of deformed algebra
• Microcanonical Jet-fragmentation in proton-proton collisions at LHC Energy
• A long-range memory stochastic model of the return in financial markets
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• Bose-Einstein condensation of light: General theory
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• Generalized information entropies depending only on the probability distribution
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• Finite-energy Lévy-type motion through heterogeneous ensemble of Brownian particles
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• Power-law statistics in the velocity fluctuations of Brownian particle in inhomogeneous media and driven by colored noise
• Modified entropies as the origin of generalized uncertainty principles
• Fokker-Planck Theory of Nonequilibrium Systems Governed by Hierarchical Dynamics
• Specific heat and entropy of $N$-body nonextensive systems
• Statistical mixing and aggregation in Feller diffusion
• Fluctuations of entropy and log-normal superstatistics
• A maximum entropy approach to H-theory: Statistical mechanics of hierarchical systems
• Superstatistics and the quest of generalized ensembles equivalence in a system with long-range interactions
• Conditional maximum-entropy method for selecting prior distributions in Bayesian statistics
• Central limit theorem for a class of globally correlated random variables
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• A superstatistical measure of distance from canonical equilibrium
• Conditional entropic approach to nonequilibrium complex systems with weak fluctuation correlation
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• Random diffusivity scenarios behind anomalous non-Gaussian diffusion
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• Bayesian approach to extreme-value statistics based on conditional maximum-entropy method
• Skewed superstatistical distributions from a Langevin and Fokker-Planck approach