Titre :

On the Relationship of Energy and Probability in Models of Classical Statistical Physics

Auteur(s) :

Dachian, Serguei [Auteur]
Tomsk State University [Tomsk]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Nahapetian, B [Auteur]

Titre de la revue :

Markov Processes And Related Fields

Pagination :

649-682

Éditeur :

Polymat Publishing Company

Date de publication :

2019

ISSN :

1024-2953

Mot(s)-clé(s) en anglais :

random field
specification
1-specification
Gibbs formula
Hamiltonian
transition energy field
one-point transition energy field

Discipline(s) HAL :

Mathématiques [math]/Physique mathématique [math-ph]
Mathématiques [math]/Probabilités [math.PR]

Résumé en anglais : [en]

In this paper we present a new point of view on the mathematical foundations of statistical physics of infinite volume systems. This viewpoint is based on the newly introduced notions of transition energy function, ...
Lire la suite >In this paper we present a new point of view on the mathematical foundations of statistical physics of infinite volume systems. This viewpoint is based on the newly introduced notions of transition energy function, transition energy field and one-point transition energy field. The former of them, namely the transition energy function, is a generalization of the notion of relative Hamiltonian introduced by Pirogov and Sinai. However, unlike the (relative) Hamiltonian, our objects are defined axiomatically by their natural and physically well-founded intrinsic properties. The developed approach allowed us to give a proper mathematical definition of the Hamiltonian without involving the notion of potential, to propose a justification of the Gibbs formula for infinite systems and to answer the problem stated by D. Ruelle of how wide the class of specifications, which can be represented in Gibbsian form, is. Furthermore, this approach establishes a straightforward relationship between the probabilistic notion of (Gibbs) random field and the physical notion of (transition) energy, and so opens the possibility to directly apply probabilistic methods to the mathematical problems of statistical physics.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL