156 EFFECT OF VARIOUS PROCESSES 



We define a path as the series of phases through which a 

 system passes in the course of time when the external co- 

 ordinates have fixed values. When the external coordinates 

 are varied, paths are changed. The path of a phase is the 

 path to which that phase belongs. With reference to any 

 ensemble of systems we shall denote by 27| p the average value 

 of the density-in-phase in a path. This implies that we have 

 a measure for comparing different portions of the path. We 

 shall suppose the time required to traverse any portion of a 

 path to be its measure for the purpose of determining this 

 average. 



With this understanding, let us suppose that a certain en- 

 semble is in statistical equilibrium. In every element of 

 extension-in-phase, therefore, the density-in-phase D is equal 

 to its path-average 27] p . Let a sudden small change be made 

 in the external coordinates. The statistical equilibrium will be 

 disturbed and we shall no longer have D ~D\ P everywhere. 

 This is not because D is changed, but because ~D\ p is changed, 

 the paths being changed. It is evident that if D > I)] p in 

 a part of a path, we shall have D < ~D\ p in other parts of the 

 same path. 



Now, if we should imagine a further change in the external 

 coordinates of the same kind, we should expect it to produce 

 an effect of the same kind. But the manner in which the 

 second effect will be superposed on the first will be different, 

 according as it occurs immediately after the first change or 

 after an interval of time. If it occurs immediately after the 

 first change, then in any element of phase in which the first 

 change produced a positive value of D - 2J| P the second change 

 will add a positive value to the first positive value, and where 

 D - 1)\ p was negative, the second change will add a negative 

 value to the first negative value. 



But if we wait a sufficient time before making the second 

 change in the external coordinates, so that systems have 

 passed from elements of phase in which D - ~D\ P was origi- 

 nally positive to elements in which it was originally negative, 

 and vice versa, (the systems carrying with them the values 



