Remarks
- The Liouville equation is valid for both equilibrium and nonequilibrium systems. It is a fundamental equation of nonequilibrium statistical mechanics. Its application to dilute gases is called the Boltzmann equation.
- The Liouville equation is integral to the proof of the fluctuation theorem from which the second law of thermodynamics can be derived. It is also the key component of the derivation of Green-Kubo relations for linear transport coefficients such as shear viscosity, thermal conductivity or electrical conductivity.
- Virtually any textbook on Hamiltonian mechanics, advanced statistical mechanics, or symplectic geometry will derive the Liouville theorem.
Read more about this topic: Liouville's Theorem (Hamiltonian)
Famous quotes containing the word remarks:
“I thought my razor was dull until I heard his speech and that reminds me of a story that’s so dirty I’m ashamed to think of it myself.”
—S.J. Perelman, U.S. screenwriter, Bert Kalmar, Harry Ruby, and Norman Z. McLeod. Groucho Marx, Horsefeathers, as a newly-appointed college president commenting on the remarks of Huxley College’s outgoing president (1932)
“So, too, if, to our surprise, we should meet one of these morons whose remarks are so conspicuous a part of the folklore of the world of the radio—remarks made without using either the tongue or the brain, spouted much like the spoutings of small whales—we should recognize him as below the level of nature but not as below the level of the imagination.”
—Wallace Stevens (1879–1955)
“I begin, then, with some remarks about ‘the meaning of a word.’ I think many persons now see all or part of what I shall say: but not all do, and there is a tendency to forget, or to get it slightly wrong. In so far as I am merely flogging the converted, I apologize to them.”
—J.L. (John Langshaw)