Issue |
Europhys. Lett.
Volume 45, Number 2, January 1999
|
|
---|---|---|
Page(s) | 149 - 155 | |
Section | General | |
DOI | https://doi.org/10.1209/epl/i1999-00139-0 | |
Published online | 01 September 2002 |
On the classical statistical mechanics of non-Hamiltonian systems
1
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
Received:
15
September
1998
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.