Superstatistical distributions from a maximum entropy principle

Abstract

We deal with a generalized statistical description of nonequilibrium complex systems based on least biased distributions given some prior information. A maximum entropy principle is introduced that allows for the determination of the distribution of the fluctuating intensive parameter $\beta$ of a superstatistical system, given certain constraints on the complex system under consideration. We apply the theory to three examples: The superstatistical quantum mechanical harmonic oscillator, the superstatistical classical ideal gas, and velocity time series as measured in a turbulent Taylor-Couette flow.

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Cited by in corpus (28)

• Generalized information and entropy measures in physics
• Superstatistics in high energy physics: Application to cosmic ray energy spectra and e+e- annihilation
• Superstatistical fluctuations in time series: Applications to share-price dynamics and turbulence
• Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion
• Generalized statistical mechanics for superstatistical systems
• Thermostatistics of deformed bosons and fermions
• Intermediate statistics as a consequence of deformed algebra
• Hierarchical maximum entropy principle for generalized superstatistical systems and Bose-Einstein condensation of light
• Bose-Einstein condensation of light: General theory
• Heterogeneous anomalous diffusion in view of superstatistics
• Multicanonical distribution: Statistical equilibrium of multiscale systems
• An intermediate distribution between Gaussian and Cauchy distributions
• Generalization of the Beck-Cohen superstatistics
• Modified entropies as the origin of generalized uncertainty principles
• Specific heat and entropy of $N$-body nonextensive systems
• Kappa distribution from particle correlations in non-equilibrium, steady-state plasmas
• Thermodynamics of the independent harmonic oscillators with different frequencies in the Tsallis statistics
• Fluctuations of entropy and log-normal superstatistics
• Time evolution of entropy associated with diffusivity fluctuations: Diffusing diffusivity approach
• A maximum entropy approach to H-theory: Statistical mechanics of hierarchical systems
• Nonextensive quantum method for itinerant-electron ferromagnetism: Fractorization approach
• Conditional entropic approach to nonequilibrium complex systems with weak fluctuation correlation
• First passage time for superstatistical Fokker-Planck models
• Skewed superstatistical distributions from a Langevin and Fokker-Planck approach
• J-measure of uncertainty (JMU) for specified probability distribution
• Statistical mechanics and Bayesian Inference addressed to the Osborne Paradox
• Bayesian inference and superstatistics to describe long memory processes of financial time series
• Crossover from anomalous to normal diffusion: truncated power-law noise correlations and applications to dynamics in lipid bilayers