On the classical statistical mechanics of non-Hamiltonian systems

Mark Tuckerman, C. J. Mundy, G. J. Martyna

Research output: Contribution to journalArticle

Abstract

A consistent classical statistical mechanical theory of non-Hamiltonian dynamical systems is presented. It is shown that compressible phase space flows generate coordinate transformations with a nonunit Jacobian, leading to a metric on the phase space manifold which is nontrivial. Thus, the phase space of a non-Hamiltonian system should be regarded as a general curved Riemannian manifold. An invariant measure on the phase space manifold is then derived. It is further shown that a proper generalization of the Liouville equation must incorporate the metric determinant, and a geometric derivation of such a continuity equation is presented. The manifestations of the nontrivial nature of the phase space geometry on thermodynamic quantities is explored.

Original languageEnglish (US)
Pages (from-to)149-155
Number of pages7
JournalEPL
Volume45
Issue number2
DOIs
StatePublished - Jan 15 1999

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statistical mechanics
Liouville equations
coordinate transformations
continuity equation
determinants
dynamical systems
derivation
thermodynamics
geometry

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

On the classical statistical mechanics of non-Hamiltonian systems. / Tuckerman, Mark; Mundy, C. J.; Martyna, G. J.

In: EPL, Vol. 45, No. 2, 15.01.1999, p. 149-155.

Research output: Contribution to journalArticle

Tuckerman, Mark ; Mundy, C. J. ; Martyna, G. J. / On the classical statistical mechanics of non-Hamiltonian systems. In: EPL. 1999 ; Vol. 45, No. 2. pp. 149-155.
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