Liouville's theorem (Hamiltonian) | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-28

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Liouville%27s_theorem_(Hamiltonian)


00:00:46 1 Liouville equations
00:11:41 2 Other formulations
00:11:51 2.1 Poisson bracket
00:14:13 2.2 Ergodic theory
00:15:12 2.3 Symplectic geometry
00:16:23 2.4 Quantum Liouville equation
00:18:46 3 Remarks
00:19:46 4 See also



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SUMMARY
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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 traveling through phase-space is constant with time.This time-independent density is in statistical mechanics known as the classical a priori probability.There are related mathematical results in symplectic topology and ergodic theory.