18 THE PHYSICAL SIGNIFICANCE OF ENTROPY 



we come to consider molecular motion in general and the inde- 

 pendence which characterizes the motion of each of the many 

 molecules we see that altogether we have here an extraordinary 

 number of degrees of freedom, and composed of such is the realm 

 of our " elementary chaos." 



If we go to the other extreme and think of only one atom, 

 we see at once that we cannot properly speak of its disorder. 

 But the case is different with a moderate number of atoms, say, 

 a hundred or a thousand. Here we surely can speak of disorder 

 if the co-ordinates of location and the velocity components are 

 distributed by haphazard among the atoms. But as the process 

 as a whole, the sequence of events in the aggregate, may not 

 with this comparatively small number of atoms take place before 

 a macroscopic observer in a unique (unambiguous) manner, 

 we cannot say that we have here reached a true state of " elemen- 

 tary chaos." If we now ask as to the minimum number of atoms 

 necessary to make the process an irreversible one, the answer is, 

 as many as are necessary to form determinate mean values which 

 will define the progress of the state in the macroscopic sense. 

 Only for these mean values does the Second Law possess signifi- 

 cance; for these, however, it is perfectly exact, just as exact as 

 the theorem of probability, which says that the mean value of 

 numerous throws with one cubical die is equal to 3 A. 



We may now properly infer from all these views that the 

 state of " elementary chaos " (or " molekular ungeordnete " 

 motion) is the necessary condition for adequate haphazard and 

 makes the application of the Theory of Probabilities possible. 



(3) Settled and Unsettled States; Distinction between Final Stage 

 of Elementary Chaos and its Preceding Stages 



The immediate purpose in the next few pages is to establish 

 the (a) distinction between the successive stages of " elementary 

 disorder " (chaos) as they develop in their inevitable passage 



