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Dynamical Systems II pp 208–254Cite as

Dynamical Systems of Statistical Mechanics

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Part of the book series: Encyclopaedia of Mathematical Sciences ((EMS,volume 2))

Abstract

The motion of a system of N particles in d dimensions is described in Statistical Mechanics by means of a Hamiltonian system of 2Nd differential equations, which generates the group of transformations of the phase space. The object of the investigation is the time evolution of probability measures on the phase space determined by this group of transformations. The principal feature of problems in Statistical Mechanics is the fact that one deals with systems consisting of a large number of particles of the same type (a mole of a gas contains 6–1023 particles). Therefore, only those results in which all estimates are uniform with respect to the number of degrees of freedom are of interest here. This restriction, which is unusual from the point of view of the standard theory of dynamical systems, specifies the mathematical feature of the problems of Statistical Mechanics.

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Authors
  1. R. L. Dobrushin
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  2. Ya. G. Sinai
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  3. Yu. M. Sukhov
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  1. Landau Institute of Theoretical Physics, ul. Kosygina 2, V-334, Moscow, USSR

    Ya. G. Sinai

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Dobrushin, R.L., Sinai, Y.G., Sukhov, Y.M. (1989). Dynamical Systems of Statistical Mechanics. In: Sinai, Y.G. (eds) Dynamical Systems II. Encyclopaedia of Mathematical Sciences, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-06788-8_10

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