Liouville's theorem: Hamiltonian flow preserves phase-space volume exactly
In Hamiltonian mechanics, the flow φ_t: (q,p) → (q(t),p(t)) is symplectic — it preserves the symplectic 2-form ω = dq∧dp. Liouville's theorem: the phase-space volume of any region is conserved under the flow. This is why statistical mechanics works — phase-space blobs stretch and fold but never compress, unlike dissipative systems.