EPL Abstract
Abstract
A consistent classical statistical mechanical theory of non-Hamiltonian
dynamical systems is presented. The nonunit Jacobian arising from the
compressibility of the underlying dynamics is reviewed. It is shown
that the dynamics generates coordinate representations in which the
metric on the space is nontrivial. It is further shown that a
proper generalization of the Liouville equation must incorporate
this metric factor, and a geometric derivation of such an equation
is presented. The resulting continuity equation is different from the
hitherto assumed form for the generalized Liouville equation.
It is then shown that an invariant measure on the space can be
defined, which, when combined with the conservation condition
on the ensemble distribution function leads to a general statement of
Liouville's theorem. Finally the manifestations of nontrivial
nature of the geometry of the phase space on the Gibbs entroy
is explored.
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