By Al Adcock

OS2U Kingfisher in motion КНИГИ ;ВОЕННАЯ ИСТОРИЯ Издательство: Squadron/Signal publicationsСерия: airplane 119Автор(ы): Al AdcockЯзык: EnglishГод издания: 1991Количество страниц: 51ISBN: 0-89747-270-5Формат: pdf (96 dpi) 1280x925Размер: 15.5 mbRapid 17

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2 The statement that the specific heat of a system goes to zero as the temperature goes to zero is known as the third law of thermodynamics. 69) Suppose that the ground state has degeneracy G 0 and energy E 0 . 71) as T → 0. In practice, it is difficult to achieve temperatures low enough to satisfy the conditions of this proof. In many cases, for higher temperatures, the specific heat goes toward zero as a power law C V ∝ T x . 74) 2 by direct use of the expression for the partition function. But E 2 − E¯ > 0 for any distribution of energy levels, so Cv = T (∂ S/∂ T )V > 0 for any system obeying the canonical density matrix.

77) e−β Eν This relation has been the subject of some rather obscure discussion in the literature. 75) give the mean square fluctuation in the pressure (times 1/kB T ). The quantity ∂ H 2 /∂ V − P 2 = ∂ H 2 /∂ V − ∂ H /∂ V ∂ H /∂ V is positive definite. 78) As long as the system is macroscopically homogeneous, the right hand side is easily seen to depend on the number of particles as N −1 so the fluctuations in the pressure are of order N −1/2 as expected. 80) for mechanical stability of a homogeneous system.

Thus the exact Microcanonical distribution 21 orbit must be space filling to an astonishing degree. One other point worth noting is that if one chooses the coordinates and momenta to be the set {Q λ }, H, t then the orbit is not convoluted at all in the space of these coordinates and momenta but is a straight line. This reveals the fact that ergodicity (or something equivalent) cannot hold for absolutely all choices of generalized coordinates and momenta. A full theory of how the microcanonical and canonical distributions arise from the microscopic orbit must take account of this and can only hope to show their validity for some overwhelmingly large set of choices of coordinates and momenta.