Stationary Solutions of Liouville Equations for Non-Hamiltonian Systems

Details Stationary Solutions of Liouville Equations for Non-Hamiltonian Systems Stationary Solutions of Liouville Equations for Non-Hamiltonian Systems

2006-02-17

arxiv.org/abs/cond-mat/0602409v1

Annals of Physics 316 (2005) 393-413

Physics

Condensed Matter

Statistical Mechanics

22 pages

Scientific paper

10.1016/j.aop.2004.11.001

We consider the class of non-Hamiltonian and dissipative statistical systems with distributions that are determined by the Hamiltonian. The distributions are derived analytically as stationary solutions of the Liouville equation for non-Hamiltonian systems. The class of non-Hamiltonian systems can be described by a non-holonomic (non-integrable) constraint: the velocity of the elementary phase volume change is directly proportional to the power of non-potential forces. The coefficient of this proportionality is determined by Hamiltonian. The constant temperature systems, canonical-dissipative systems, and Fermi-Bose classical systems are the special cases of this class of non-Hamiltonian systems.

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