Family of Probability Distributions Derived from Maximal Entropy Principle with Scale Invariant Restrictions

Abstract

Using statistical thermodynamics, we derive a general expression of the stationary probability distribution for thermodynamic systems driven out of equilibrium by several thermodynamic forces. The local equilibrium is defined by imposing the minimum entropy production and the maximum entropy principle under the scale invariance restrictions. The obtained probability distribution presents a singularity that has immediate physical interpretation in terms of the intermittency models. The derived reference probability distribution function is interpreted as time and ensemble average of the real physical one. A generic family of stochastic processes describing noise-driven intermittency, whose stationary density distribution coincides exactly with the one resulted from entropy maximization, is presented.

5 pages, No figures; Physical Review E (2013) - Brief Communication

References in corpus (5)

• Identification of direct residue contacts in protein-protein interaction by message passing
• Low frequency noise controls on-off intermittency of bifurcating systems
• Hierarchical maximum entropy principle for generalized superstatistical systems and Bose-Einstein condensation of light
• Measurement scale in maximum entropy models of species abundance
• The thermodynamics of urban population flows

Cited by in corpus (4)

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• Reference Distribution Functions for Magnetically Confined Plasmas from the Minimum Entropy Production Theorem and the MaxEnt Principle, subject to the Scale-Invariant Restrictions
• Derivation of Reference Distribution Functions for Tokamak-plasmas by Statistical Thermodynamics