### 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 language | English (US) |
---|---|

Pages (from-to) | 149-155 |

Number of pages | 7 |

Journal | EPL |

Volume | 45 |

Issue number | 2 |

DOIs | |

State | Published - Jan 15 1999 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*EPL*,

*45*(2), 149-155. https://doi.org/10.1209/epl/i1999-00139-0

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

Research output: Contribution to journal › Article

*EPL*, vol. 45, no. 2, pp. 149-155. https://doi.org/10.1209/epl/i1999-00139-0

}

TY - JOUR

T1 - On the classical statistical mechanics of non-Hamiltonian systems

AU - Tuckerman, Mark

AU - Mundy, C. J.

AU - Martyna, G. J.

PY - 1999/1/15

Y1 - 1999/1/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0033554903&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033554903&partnerID=8YFLogxK

U2 - 10.1209/epl/i1999-00139-0

DO - 10.1209/epl/i1999-00139-0

M3 - Article

AN - SCOPUS:0033554903

VL - 45

SP - 149

EP - 155

JO - Europhysics Letters

JF - Europhysics Letters

SN - 0295-5075

IS - 2

ER -