Stochastic invertible mappings for Tsallis distributions

Christophe Vignat; A. Plastino

doi:10.1016/j.crhy.2006.01.012

Stochastic invertible mappings for Tsallis distributions
[Mappings stochastiques inverses pour les distributions de Tsallis]

Christophe Vignat ¹ ; A. Plastino ^2,³

¹ Laboratoire de Production Microtechnique, E.P.F.L., Lausanne, Switzerland
² La Plata Physics Institute, Exact Sciences Faculty, National University La Plata, La Plata, Argentina
³ Argentine National Research Council—CONICET, C. C. 727, 1900 La Plata, Argentina

Comptes Rendus. Physique, Statistical mechanics of non-extensive systems, Volume 7 (2006) no. 3-4, pp. 442-448.

Résumé
Abstract

Nous définissons des relations bijectives entre les distributions Gaussiennes et les distributions de Tsallis ; à un vecteur aléatoire X suivant une distribution de Tsallis, il est possible d'associer un vecteur aléatoire Gaussien N de la façon suivante : $N = a X$ où a est une variable aléatoire indépendante de X dont nous caractérisons les propriétés. Nous montrons que cette association est bijective et construisons explicitement l'association inverse. Nous appliquons ce résultat au problème du principe zéro de la thermodynamique tel qu'il se pose dans le cadre des statistiques de Tsallis.

We devise mappings between Gaussian distributions and power-law distributions, nowadays also called Tsallis distributions. To a given Tsallis distributed vector X, one can associate a Gaussian distributed vector N in the fashion $N = a X$ where a is a random variable independent of X whose properties we are going to characterize here. We not only show that this mapping is invertible but also construct the adequate inversion operation. As an application of this stochastic mapping, we revisit the problem posed to Tsallis practitioners by the zeroth law of thermodynamics, that has bedeviled them for 15 years.

Publié le : 2006-04-01

DOI : 10.1016/j.crhy.2006.01.012

Keywords: Superstatistics, Stochastic mappings, Tsallis entropies
Mots-clés : Suprastatistiques, Application stochastique, Entropie de Tsallis

Affiliations des auteurs :

Christophe Vignat ¹ ; A. Plastino ^{2, 3}

¹ Laboratoire de Production Microtechnique, E.P.F.L., Lausanne, Switzerland
² La Plata Physics Institute, Exact Sciences Faculty, National University La Plata, La Plata, Argentina
³ Argentine National Research Council—CONICET, C. C. 727, 1900 La Plata, Argentina

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     title = {Stochastic invertible mappings for {Tsallis} distributions},
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     pages = {442--448},
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     number = {3-4},
     year = {2006},
     doi = {10.1016/j.crhy.2006.01.012},
     language = {en},
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Christophe Vignat; A. Plastino. Stochastic invertible mappings for Tsallis distributions. Comptes Rendus. Physique, Statistical mechanics of non-extensive systems, Volume 7 (2006) no. 3-4, pp. 442-448. doi : 10.1016/j.crhy.2006.01.012. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2006.01.012/

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