On the classical statistical mechanics of non-Hamiltonian systems

M. E. Tuckerman, C. J. Mundy, G. J. Martyna

Research output: Contribution to journalArticlepeer-review


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
JournalEurophysics Letters
Issue number2
StatePublished - Jan 15 1999

ASJC Scopus subject areas

  • General Physics and Astronomy


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