﻿832 Messrs. C. G. Darwin anal R. H. Fowler on 



some such argument as this is necessary to justify the 

 use of " thermodynamic probability/' the quantity used 

 with success by so many writers. 



The argument of this section has really been dealing 

 entirely with the junction of assemblies which had the 

 same temperature ; it may be more conveniently visualised 

 as dealing with the separation of an assembly into parts 

 which are thereafter isolated from one another. Actually 

 of course our work must include the fact that entropy has 

 the property of increasing when assemblies at different 

 temperatures are joined. We have not yet .had cause to 

 discuss this, as we have so far been mainly criticizing theories 

 which were developed by considering only assemblies of the 

 same temperature. 



§ 5. Entropy as a non-fluctuating quantity. 



The kinetic entropy as defined above is a fluctuating 

 quantity, whether we find it for the whole assembly or 

 for a part. On the other hand, the entropy of thermo- 

 dynamics is a function of the state of the assembly and 

 must be regarded as constant, and we must see how the 

 two may be best related. Now we cannot get away entirely 

 from the question of fluctuations, but we can conveniently 

 simplify the definition so as to dissociate them from the 

 entropy. Consider an assembly composed of A's and B's. 

 At every moment its state is specih'ed by the values of 



a , ^,.'..60, b 1 , and these numbers all fluctuate, and 



with them the energy Ea and the kinetic entropy Sa- But 

 if we want to treat of the entropy of the A's as opposed to 

 that of the IVs, we must suppose the A's to be suddenly 

 isolated. After the isolation they will have a certain 

 definite energy determined by the chance state at the 

 moment of isolation, and this energy will determine the 

 temperature and so the thermodynamic entropy. So, to 

 define a function representing the thermodynamic entropy, 

 it is most reasonable to choose some simple non-fluctuating 

 function of the state of the whole assembly; we can then 

 allow for the fluctuations in the entropy of its parts by 

 imagining them suddenly isolated, and calculating their 

 entropies from the energies they chance to have at the 

 moment of isolation on the same principle as was previously 

 done for the whole assembly. There are several suitable 

 definitions — for example, we can use the total number of 

 the complexions, or the average number, or the maximum 



