Bayesian approach to superstatistics

F. Sattin

Research output: Contribution to journalArticle

38 Citations (Scopus)


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/β) 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 e-βE, but β varies from cell to cell, with its own probability density f(β). 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 β 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(β), that was not fully elucidated till now.
Original languageEnglish
Pages (from-to)219 - 224
Number of pages6
JournalEuropean Physical Journal B
Issue number2
Publication statusPublished - Jan 2006
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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