Airco DH.10

Airco DH.10 КНИГИ ;ВОЕННАЯ ИСТОРИЯ Издательство: Albatros - Windsock DataFile 038Серия: Windsock DataFile 038Язык: английскийКоличество страниц: 38Формат: PDFРазмер: 28.94 Мб eighty five

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Of particles in a etc. ,im)C{1 .... ,qm-ql) , then it 40 will also be invariant when the qi+q q E R d. If moreover U(ql ..... qm ) = 0 qi as soon as ! ,! ,qm) for some i # j can be split into R, so that then (q',q") U(q) with U(q) = U(q') + U(q"). U(q) defined for finite configurations q having these properties: a) U is symmetric when particles are permuted. b) U is invariant under translations of the configurations in c) U is of finite range R ~ r, R d" as defined above. This last assumption can be relaxed, but it simplifies the arguments considerably.

On a scale q = L-x , which there is a non trivial variation of these macroscopic Consider now the state in a macroseopieally side L-Ax value is centered at U(x) N-U(x). L-x . infinitesimal G is extensive as g(8,~) = lim gA(8,wIy) A effect coming from y. )- converges to as L ~ ~ with Ax fixed. formula for a non ideal gas. To see how g(8,~) let us independently of our previous formulas define it by the macroscopic ~Ap Hence we can x the pressure can be expressed in terms of AX = when these exist (which happens conclude that the average density at nn(X) = 8 -I BgA (B'U-U(x)Iy) SU gA(~,uly) A + ~, so that except at most for denumer~bly many va~iues of n(x) with constant - log GA(~,uly) Moreover, A in the cell, so its contribution to the energy in the cell Now, as we shall prove later, it is a basic fact that also = ~ cell The potential has the esseDtially The partition function GA(B,u-U(xlly) 1 on quantities.

Of particles. will be a I = 8, region of e. D g a 2 = -8~, and differentiable UI special case to be t r e a t e d is equal to the total energy Then the parameters and we will show that there, s(e,n) aI > -~ and that it is an increasing and H, a2 in an open function is given by g(8,~) = sup (s(e,n) - 8e + 8wn), e,n and will be shown to be finite when 8 > 0 , ~ arbitrary. Since s(e,n) is 58 differentiable the values of e,n the equations 8~ = -s~(e,n) 8 = s~(e,n) , g(8,U) = s(e,n) - 8e + ~ n the relation .

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