**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 systemâ€“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.

Read more about Liouville's Theorem (Hamiltonian): Liouville Equations, Physical Interpretation, Remarks

### Famous quotes containing the word theorem:

“To insure the adoration of a *theorem* for any length of time, faith is not enough, a police force is needed as well.”

—Albert Camus (1913–1960)