  For statistical mechanics we need to consider a microscopic state space and a dynamical evolution of states in that space. Classically this will be a phase space, with an N-body system having 3N position degrees of freedom and 3N momentum degrees of freedom. A single point in the phase space corresponds to the combined physical state of all the N bodies. The dynamics is almost always supposed to be Hamiltonian. A Hamiltonian flow preserves the measure dX3NdP3N.  This measure can be used to define the volume, VR, of a region of phase space, R, as: