Liouville's Theorem (Hamiltonian)

Liouville's Theorem (Hamiltonian)

In physics, Liouville's theorem, named after the French mathematician Joseph Liouville, is a key theorem in classical statistical and Hamiltonian mechanics. It asserts that the phase-space distribution function is constant along the trajectories of the system–that is that the density of system points in the vicinity of a given system point travelling through phase-space is constant with time.

There are also related mathematical results in symplectic topology and ergodic theory.