Phase space volume is the volume of a region of possible states in the phase space of a dynamical
system. In Euclidean coordinates it is ordinary Lebesgue
measure. A region 
transported by a smooth flow 
has volume
 |
where 
is the matrix of first derivatives
of the flow and its determinant
is the Jacobian. If the generating vector
field has constant divergence 
, then 
. Thus negative
divergence contracts phase space volume, as in the
Chen-Lee system. The flow
of a Hamiltonian system preserves phase space
volume in canonical coordinates by Liouville's
phase space theorem (Arnold 1989).
