## 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) |
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Pages (from-to) | 149-155 |

Number of pages | 7 |

Journal | Europhysics Letters |

Volume | 45 |

Issue number | 2 |

DOIs | |

State | Published - Jan 15 1999 |

## ASJC Scopus subject areas

- General Physics and Astronomy