Volume 45, Number 2, January 1999
|Page(s)||149 - 155|
|Published online||01 September 2002|
On the classical statistical mechanics of non-Hamiltonian systems
Department of Chemistry and Courant Institute of Mathematical
Sciences New York University - New York, NY 10003, USA
2 Max-Planck Institut für Festkörperforschung Heisenbergstrasse 1, 70569 Stuttgart, Germany
3 Department of Chemistry, Indiana University - Bloomington, IN 47405, USA
Accepted: 15 November 1998
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.
PACS: 05.20.-y – Statistical mechanics / 02.40.-k – Geometry, differential geometry, and topology / 31.15.Qg – Molecular dynamics and other numerical methods
© EDP Sciences, 1999
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