160 EFFECT OF VARIOUS PROCESSES 



the thermal contact of two bodies may increase but cannot 

 diminish the sum of their entropies. 



Let us especially consider the case in which the two original 

 ensembles were both canonically distributed in phase with the 

 respective moduli j and 2 . We have then, by Theorem III 

 of Chapter XI, 



nJ + ^ < r?i" + |- (464) 



^' + !'<^" + ^ (465) 



Whence with (463) we have 





_ 



If we write W for the average work done by the combined 

 systems on the external bodies, we have by the principle of 

 the conservation of energy 



W = ' - M " = / - X " + e 2 ' - e 2 ". (468) 



Now if TFis negligible, we have 



e/' _ e/ = - (e"" - ?) (469) 



and (467) shows that the ensemble which has the greater 

 modulus must lose energy. This result may be compared to 

 the thermodynamic principle, that when two bodies of differ- 

 ent temperatures are brought together, that which has the 

 higher temperature will lose energy. 



Let us next suppose that the ensemble E% is originally 

 canonically distributed with the modulus @ 2 , but leave the 

 distribution of the other arbitrary. We have, to determine 

 the result of a similar process, 



