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The q-exponential family in statistical physics

100%
Naudts J.
Open Physics
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2009
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vol. 7
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issue 3
405-413
EN
The notion of a generalized exponential family is considered in the restricted context of non-extensive statistical physics. Examples are given of models belonging to this family. In particular, the q-Gaussians are discussed and it is shown that the configurational probability distributions of the micro-canonical ensemble belong to the q-exponential family.
2
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Conditional approach to thermo-superstatistics

100%
Abe S.
Open Physics
|
2009
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vol. 7
|
issue 3
401-404
EN
A conditional approach is developed for establishing a generalized thermodynamic-like formalism for superstatistical systems. In this framework, the existence of two largely-separated time scales is explicitly taken into account. A generalization of Einstein’s relation for fluctuations is derived based on the restricted conditional maximum-entropy method.
3
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Lévy flights and Lévy-Schrödinger semigroups

100%
Garbaczewski P.
Open Physics
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2010
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vol. 8
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issue 5
699-708
EN
We analyze two different confining mechanisms for Lévy flights in the presence of external potentials. One of them is due to a conservative force in the corresponding Langevin equation. Another is implemented by Lévy-Schrödinger semigroups which induce so-called topological Lévy processes (Lévy flights with locally modified jump rates in the master equation). Given a stationary probability function (pdf) associated with the Langevin-based fractional Fokker-Planck equation, we demonstrate that generically there exists a topological Lévy process with the same invariant pdf and in reverse.
4
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Gauss’ law of error revisited in the framework of Sharma-Taneja-Mittal information measure

100%
Scarfone A., Suyari H., Wada T.
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EN
We reformulate the Gauss’ law of error in presence of correlations which are taken into account by means of a deformed product arising in the framework of the Sharma-Taneja-Mittal measure. Having reviewed the main proprieties of the generalized product and its related algebra, we derive, according to the Maximum Likelihood Principle, a family of error distributions with an asymptotic power-law behavior.
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