Let us for sake of brevity speak of the state of permanence finally attained by this chaotic mass as the normal state, and all the preceding chaotic states as abnormal states.
[24]The rest of the paragraph is a repetition of what was stated at middle of [p. 19].
(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 backward to bring about, in reverse order, the finite physical state which initiated them; for the effecting of such an opposite change would demand a co-operation and concert of action on the part of the elementary constituents which is felt to be quite impossible. It will not be so general and scientific, but perhaps more easily apprehended, if we put this result in terms of human effort, namely, "by asserting that any process is irreversible we assert that by no means within our present or future power can we reverse it, i.e., we cannot control the individual molecules."
SECTION C
ENTROPY
We have seen above that the inevitable growth in the number of complexions is the mark of irreversibility; the number of complexions at any stage can also in a certain sense be regarded as the measure, index or determinant of that stage or state of the system of elements under consideration. Any function of the number of complexions can be regarded as such measure, index or determinant. Now it has been shown by BOLTZMANN that the expression found thermodynamically for the quantity called entropy differs only by a physically insignificant constant from the logarithm of said number of complexions. But the latter may properly be regarded as a true measure of the probability of the system being in the state considered. BOLTZMANN has defined the entropy of a physical system as the logarithm of the probability of the mechanical condition of the system and PLANCK has cast it into the numerical form,
where