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properties with the thermodynamic entropy. These properlies are : 



1. For reversible changes from one stale of equilibrium into the 



dQ 

 other is — the differential ol a quantity which is defined as entropy j 



2. in an isolated system which, as a whole, is not in equilibrium, 

 bul may be divided into parts which are, the total entropy 

 increases. We saw above that in general the quantity introduced by 



BOLTZMANN 



II — | j / log f do doj 



decreases, also when the system does not consist of parts, each in 

 itself in equilibrium. So if we consider a quantity proportional to 

 — H as entropy, it will certainly satisfy the second condition in by 

 far the majority of cases. As to the first condition, this is satisfied 



2 

 as Lorentz has shown"), if — - f i is taken for the constant by which 



jj . ... .. , . ... mean kin. energy per mol. 



H is multiplied, m which it = - — r— . ror a 



abs. temperature 



gas in stationary state 



so that 



2 2 

 nil— 



3 f 3 



li N f log C -■ -J 



2 2 3m 



= — H Nlog v -f ii N log »> - n A' log N — a N log - • -f tiX 



3 3 ' 4.T/i 



for which Lorentz writes : 



— u N log v \- (i N log ih \- ( ". 

 o 



f N \ 



At a given temperature we may, accordingly, write A /<<</ |- C J 



also for //, in which C still contains th, no longer A 7 and v. 



Besides this entropy of Boltzmann different quantities have heen 

 kinetically defined by Gibbs, which, according to him, possess the pro- 

 perties of the entropy. The most prominent of them is the - r t or 



— IPlogPdr, being the negative mean log of the density over the 

 canonical ensemble which represents the system in equilibrium. As 

 ~~*)~W. I.e. Abliundlung VIII. 



