Family of probability distributions derived from maximal entropy principle with scale invariant restrictions

Giorgio Sonnino, György Steinbrecher, Alessandro Cardinali, Alberto Sonnino, Mustapha Tlidi

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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, where the stationary density distribution coincides exactly with the one resulted from entropy maximization, is presented. © 2013 American Physical Society.
Original languageEnglish
Article number014104
Pages (from-to)-
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number1
Publication statusPublished - 31 Jan 2013
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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