Multicanonical distribution: statistical equilibrium of multiscale systems

A multicanonical formalism is introduced to describe the 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 p...

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Bibliographic Details
Published inPhysical review. E, Statistical, nonlinear, and soft matter physics Vol. 86; no. 5 Pt 1; p. 050103
Main Authors Salazar, Domingos S P, Vasconcelos, Giovani L
Format Journal Article
LanguageEnglish
Published United States 01.11.2012
Subjects
Acceleration
Algorithms
Computer Simulation
Models, Statistical
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Summary:A multicanonical formalism is introduced to describe the 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.
ISSN:1550-2376
DOI:10.1103/PhysRevE.86.050103