Bayesian approach to superstatistics

Abstract

The superstatistics approach recently introduced by Beck [C. Beck and E.G.D. Cohen, Physica A 322, 267 (2003)] is a formalism that aims to deal in a unifying way with a large variety of complex nonequilibrium systems, for which spatio-temporal fluctuations of one intensive variable (the "temperature" 1/b) are supposed to exist. The intuitive explanation provided by Beck for superstatistics is based on the ansatz that the system under consideration, during its evolution, travels within its phase space which is partitioned into cells. Within each cell, the system is described by ordinary Maxwell-Boltzmann statistical mechanics, i.e., its statistical distribution is the canonical one, but b varies from cell to cell, with its own probability density f(b). In this work we first address that the explicit inclusion of the density of states in this description is essential for its correctness. The correction is not relevant for developments of the theory, but points to the fact that its correct starting point, as well its meaning, must be found at a more basic level: the pure probability product rule involving the intensive variable b and its conjugate extensive one. The question therefore arises how to assign a meaning to these probabilities for each specific problem. We will see that it is easily answered through Bayesian analysis. This way, we are able to provide an interpretation for f(b), that was not fully elucidated till now.

13 pages. To be published in The European Physics Journal B

References in corpus (6)

• Coarse-grained distributions and superstatistics
• Velocity difference statistics in turbulence
• Superstatistics in random matrix theory
• Non-Gaussian PDFs from Maximum-Entropy-principle considerations
• The PDF of fluid particle acceleration in turbulent flow with underlying normal distribution of velocity fluctuations
• Superstatistics from a different perspective

Cited by in corpus (28)

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• Beyond Boltzmann-Gibbs statistics: Maximum entropy hyperensembles out-of-equilibrium
• Tsallis Distribution Decorated With Log-Periodic Oscillation
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• Fluctuations, correlations and the nonextensivity
• Example of a possible interpretation of Tsallis entropy
• The imprints of superstatistics in multiparticle production processes
• Some intriguing aspects of multiparticle production processes
• Quasi-power laws in multiparticle production processes
• Temperature is not an observable in superstatistics
• Equivalence of volume and temperature fluctuations in power-law ensembles
• Generalization of the Beck-Cohen superstatistics
• On thermodynamic self-consistency of generic axiomatic-nonextensive statistics
• Emergence of Tsallis statistics as a consequence of invariance
• Superstatistics and temperature fluctuations
• Kappa distribution from particle correlations in non-equilibrium, steady-state plasmas
• 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
• Bistable stochastic processes in the q-exponential family
• On the possible distributions of temperature in nonequilibrium steady states
• Nonequilibrium thermodynamics of uncertain stochastic processes
• Imprints of energy limitation in transverse momentum distributions of jets
• A superstatistical measure of distance from canonical equilibrium
• Conditional maximum entropy and Superstatistics
• Relaxation and correlation times of nonequilibrium multiparticle systems
• Superstatistics as the thermodynamic limit of driven classical systems
• Fundamental temperature exclusively determines the validity of superstatistics
• Kappa distributions in the framework of superstatistics