Title :

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

Author(s) :

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

Journal title :

Markov Processes And Related Fields

Pages :

649-682

Publisher :

Polymat Publishing Company

Publication date :

2019

ISSN :

1024-2953

English keyword(s) :

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

HAL domain(s) :

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

English abstract : [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, ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL