Remarks
The thesis of this theorem of classical mechanics reads exactly as the heat theorem of thermodynamics. This fact shows that thermodynamic-like relations exist between certain mechanical quantities in multidimensional ergodic systems. This in turn allows to define the "thermodynamic state" of a multi-dimensional ergodic mechanical system, without the requirement that the system be composed of a large number of degrees of freedom. In particular the temperature is given by twice the time average of the kinetic energy per degree of freedom, and the entropy by the logarithm of the phase space volume enclosed by the constant energy surface (i.e. the so-called volume entropy.
Read more about this topic: Generalized Helmholtz Theorem
Famous quotes containing the word remarks:
“There are remarks that sow and remarks that reap.”
—Ludwig Wittgenstein (1889–1951)
“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)
“Where do whites fit in the New Africa? Nowhere, I’m inclined to say ... and I do believe that it is true that even the gentlest and most westernised Africans would like the emotional idea of the continent entirely without the complication of the presence of the white man for a generation or two. But nowhere, as an answer for us whites, is in the same category as remarks like What’s the use of living? in the face of the threat of atomic radiation. We are living; we are in Africa.”
—Nadine Gordimer (b. 1923)