Phase space flows for non-Hamiltonian systems with constraints
Statistical Mechanics
2009-11-11 v1
Abstract
In this paper, non-Hamiltonian systems with holonomic constraints are treated by a generalization of Dirac's formalism. Non-Hamiltonian phase space flows can be described by generalized antisymmetric brackets or by general Liouville operators which cannot be derived from brackets. Both situations are treated. In the first case, a Nos\'e-Dirac bracket is introduced as an example. In the second one, Dirac's recipe for projecting out constrained variables from time translation operators is generalized and then applied to non-Hamiltonian linear response. Dirac's formalism avoids spurious terms in the response function of constrained systems. However, corrections coming from phase space measure must be considered for general perturbations.
Cite
@article{arxiv.cond-mat/0508192,
title = {Phase space flows for non-Hamiltonian systems with constraints},
author = {Alessandro Sergi},
journal= {arXiv preprint arXiv:cond-mat/0508192},
year = {2009}
}