J. Chem. Phys. Abstract
Abstract
The use of non-Hamiltonian dynamical systems to perform
molecular dynamics simulation studies is becoming
standard. However, the lack of a sound statistical
mechanical foundation for non-Hamiltonian systems has caused
numerous misconceptions about the phase space distribution
functions generated by these systems to appear in the literature.
Recently a rigorous classical
statistical mechanical theory of non-Hamiltonian systems has been derived,
[M. E. Tuckerman, et al, Europhys. Lett. 45, 149 (1999)].
In this paper, the new theoretical formulation is employed to develop
the non-Hamiltonian generalization of the usual
Hamiltonian based statistical mechanical phase space principles.
In particular, it is shown how the invariant phase
space measure and the complete sets of conservation laws
of the dynamical system can be combined with the generalized
Liouville equation for non-Hamiltonian systems to produce
a well defined expression for the phase space distribution function.
The generalization provides a systematic,
controlled procedure for designing non-Hamiltonian
molecular dynamics algorithms
which can be used to generate non-microcanonical ensembles, stationary
non-equilibrium flows and/or the dynamics of constrained systems.
In light of this new general analysis,
molecular dynamics algorithms for the canonical and isothermal-isobaric
ensembles are examined, potential difficulties illuminated,
and the limitations of previous theoretical treatments elucidated.