Multicanonical distribution: Statistical equilibrium of multiscale systems

Abstract

A multicanonical formalism is introduced to describe statistical equilibrium of complex systems exhibiting a hierarchy of time and length scales, where the hierarchical structure is described as a set of nested "internal heat reservoirs" with fluctuating "temperatures." The probability distribution of states at small scales is written as an appropriate averaging of the large-scale distribution (the Boltzmann-Gibbs distribution) over these effective internal degrees of freedom. For a large class of systems the multicanonical distribution is given explicitly in terms of generalized hypergeometric functions. As a concrete example, it is shown that generalized hypergeometric distributions describe remarkably well the statistics of acceleration measurements in Lagrangian turbulence.

11 pages, 1 figure

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• A maximum entropy approach to H-theory: Statistical mechanics of hierarchical systems
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• Eigenvalue Distribution of Empirical Correlation Matrices for Multiscale Complex Systems and Application to Financial Data
• First passage time for superstatistical Fokker-Planck models
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