86 THE PHYSICAL SIGNIFICANCE OF ENTROPY 



finally attained by this chaotic mass as the normal state, and all 

 the preceding chaotic states as abnormal states. 



(3) Number of complexions, or probability, of a chaotic state. 



It was shown, in an earlier portion of this presentation, that 

 each such chaotic state (abnormal or normal) is characterized 

 by its number of complexions, which is determined by the Theory 

 of Probabilities. This number is a variable one for the successive 

 abnormal states and is a fixed and a maximum one (under given 

 external conditions) for the normal state. Now BOLTZMANN 

 (by the application of the Theory of Probabilities to this chaotic 

 state) has shown that the means of these states vary in one direction 

 only, in such a way that the probable number of complexions 

 of the successive abnormal states continually grows till it attains 

 its maximum in the normal and permanent state. 



SECTION B 

 IRREVERSIBILITY 



This one-sidedness of the average action or flux constitutes and 

 sharply defines what is meant by irreversibility. It does not 

 imply that the motion of any particular atom cannot be reversed, 

 but that the order in which these averages (or the number of 

 complexions) occur cannot be reversed. We have here a process, 

 consisting of a number of separately reversible processes, which 

 proves to be irreversible in the aggregate. This is not the only 

 possible characterization of the property of irreversibility inherent 

 in all natural events, but is perhaps as general and exact a one 

 as can be enunciated. Superficially speaking, from the confused 

 and irregular motions contemplated, it is quite evident that this 

 succession of whirls and eddies cannot be worked directly back- 

 ward to bring about, in reverse order, the finite physical state 

 which initiated them; for the effecting of such an opposite change 



