Appendix to Section 23 Nonstationary distributions of density in T-space

Appendix to Section 23 Nonstationary distributions of density in T-space 

The analysis of Krod shows in fact that for t= + x p lies closer to the ergodic distribution given in Eq. (30) than at t=ta and that similarly 2(0 lies closer to the corresponding 2 value at = + .222 However, it would be a mistake to confound this result, which corresponds to statement (XV) in Section 23d, with the assertion that for t— + the ergodic distribution and the corresponding 2 value are approximately attained. The latter corresponds to Gibbs s indispensable statement (XV ). It is precisely for the periodic systems treated by Krod that it is particularly easy to see that the transition from (XV) to (XV ) necessarily invokes an assumption similar to the ergodic hypothesis.224 (Cf. the remarks in Sections 23a and 23b). 

Appendixes to Sections 24 ond 25 The analogy to the observable behavior of thermodynamic systems and Articles following or related to Gibbs1 s treatment 

A) Theorem of union If two systems have the same kinetic energy per degree of freedom before they are in contact with each other, this will remain the case after the contact. 

B) Theorem of separation If we consider a system which consists of two bodies in contact and we separate this system into its two constitutents, both of these parts will have the same kinetic energy per degree of freedom as the previously united system had. 

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