Statistical Thermodynamics by E. Schrodinger

By E. Schrodinger

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J, ... th group). Interpret this result. Show that the 8ntropy is R S -kf~lnGi s: Pi = 0 for all i. * and prove that the 8ntropy production rate satisfies H: S ~ 0 if the principle of microscopic reversibility M (A ij Aii for all i, j) holds. ) = L GjAji G;( i- G. -~F;. p, J J I (c) The principles X and P clearly imply Pi 0 if we take into account the results of part (b). If the principle P holds, the W groups of states decompose into a smaller number of classes of states between which transitions are not possible.

I = 1 Clearly j can assume all positive integral values or zero. Given one of these, the degeneracy gj of this level is given by the following number theory problem: gj is the number of ways of expressing an integer j as a sum of w integers, zero and repetitions being aIlowed and order being important. This in turn is clearly the same as the number of ways of placing j indistinguishable balls into w distinguishable boxes. (w - I )! Y) Note that the ground state j = 0 is always non-degenerate, go 1.

Y1T. for the chemical constant. 12 as follows. The distributions are then referred to as non-degenerate. Show that in the classical approximation (JL -lo- -(0) =tj~. ~I­ F+kTlnZ as required. (f) This result follows from a alnZ I (e) We have U-TS+pv exp[;~(JL-Ej)l'J ... 13 2 = 41Tvgp dp 3 h v(2Em)mdE and the quoted result follows. ~ +In[(21Tm)%k7l gh- 3 j. (d) Substitute the expression for p from part (b) into that for the entropy: S = k(n >(s + 2 k(n>[s+2 :T) (n > Solution (n> TS ns+l}. D :;: res + 1)/(0, s + 1, ± )/(S+ 2 A/v, show that if p (s+ l)pv 0 (s+ l)vDp+2 A(kT)S A = 81TVh- 3 c- 3 , where c is the velocity oflight.

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