Stationary Solutions of Liouville Equations for Non-Hamiltonian Systems
Statistical Mechanics
2009-11-11 v1 Mathematical Physics
math.MP
Adaptation and Self-Organizing Systems
Classical Physics
Abstract
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.
Keywords
Cite
@article{arxiv.cond-mat/0602409,
title = {Stationary Solutions of Liouville Equations for Non-Hamiltonian Systems},
author = {Vasily E. Tarasov},
journal= {arXiv preprint arXiv:cond-mat/0602409},
year = {2009}
}
Comments
22 pages