But of course, the full equivalent of entropy can be substituted as a universal measure of irreversibility. On [p. 27] we have pointed out that the number of complexions included in a given state can be defined as the probability W of the state, then in a footnote, attention is called to the identity of entropy with the logarithm of this state of probability = logarithm of the number of complexions of the state. This makes entropy a function of the number of complexions, so that one may in this sense be regarded as the equivalent of the other. We may now properly speak of the number of complexions of a state as the universal measure of its irreversibility. The physical meaning of irreversibility becomes apparent when put in this form. The greater the number of complexions included in a state the more disordered is its elementary condition and the more difficult (more impossible, so to speak), is it to directly so influence the constituents of the whole that they will reverse the sequence of the mean values the aggregate tends of itself to assume. An illustration will help to make this clear; the irreversible case in which work (i.e., friction) is converted into heat. "For example, the direct reversal of a frictional process is impossible because this would presuppose the existence of an elementary order among adjacent, mutually interacting molecules. For then it must predominantly be the case that the collisions of each pair of molecules must bear a certain distinguishable character inasmuch as the velocities of two colliding molecules must always depend in a determinate manner on the place where they meet. Only thereby can it be attained that there will result from the collisions predominantly like directed velocities."
The outcome of the whole study of irreversibility results in the briefly stated law: "There exists in Nature a quantity which changes always in the same sense in all natural processes."
This boldly asserts the essential one-sidedness of Nature. The proposition stated in this general form may be correct or incorrect; but whichever it may be it will remain so independently of human experimental skill.
[SECTION D]
(1) The Gradual Development of the Idea that Entropy Depends on Probability
Entropy is difficult to conceive, in that, as it does not directly affect the senses, there is nothing physical to represent it; it cannot be felt like temperature. It has no analogue in the whole of Physics; Zeuner's heat weight will perhaps serve as such for reversible states, but is inadequate for irreversible ones. This is not surprising when we consider the outcome, namely, that it depends on probability considerations.
CLAUSIUS coined the term Entropy from the Greek, from a word meaning transformation; with him the transformation value was equal to the difference between the entropy of the final and initial states. As there is a general expression for entropy, we can readily write the equivalent of any transformation between two particular states.
Strictly speaking, however, entropy by itself depends only on the state in question, not on any change it may experience, nor on its past history before reaching the state contemplated. Of course, this was appreciated by such a master mind as CLAUSIUS, and, indeed, he defined the entropy as the algebraic sum of the transformations necessary to bring a body into its existing state. Moreover, as the formula for it was in terms of other more or less sensible thermodynamic quantities, its relation to these was at first more readily grasped, could be represented diagrammatically, and had to do duty for the true, but still unknown, physical idea of entropy itself. It was early understood, too, that growth of entropy was closely connected with the degradation or waste of energy; that it was identical with the Second Law. The frequently given, but not always valid, relation,
[17] led to entropy being called a factor of energy. But all these were change relations and did not go to the root of the difficulty, as to what constituted the physical nature of unchanged entropy.