The conservative statement under (1) is confessedly based on the Calculus of Probabilities as applied to a mechanical system. We repeat here therefore what was said about (4) of the preceding series of equivalents, namely, that the number of complexions of the state is a necessary feature of this statement of the second law and therefore constitutes its physical significance.
The statement under (2) is a common one. As each of the exact definitions of the entropy for every natural event has been shown to depend solely on the number of complexions of a system (all the bodies participating in the event being considered a part of the system) we have here likewise in this number an adequate physical explanation of the second law.
Statements (3), (8) and (9) have already been derived and explained in this presentation (see pp. [45], [46]) as the result of the growth of the number of complexions in every natural event, when all the bodies participating in the event are considered.
Statement (4) is only a slight variation of (3) and needs no special comment here.
The same may be said of the three forms under (5).
The statement in (6) is only a corollary resulting from the use of (3) or (4) or (5).
The statement in (7) of the second law may be objected to because the underlying definitions are not entirely free from ambiguity and because it lacks a scientifically general character. But it expresses compactly a matter of great consequence in technical circles. Moreover its explanation in our physical terms is very simple and direct, viz., when waste is incurred there is a growth in the number of complexions, the complexity of the molecular motions has been increased. Less of the stored-up energy is available, less is capable of being directed into certain technical channels. Evidently the greater the complexity of the molecular motions the less governable they are by any direct external force or influence we can bring to bear. This is because we are unable to act directly on the individual molecules and sway them to our special technical purpose. Our external forces and agencies can only operate on the aggregates comprising our system and must obey the one-sided law imposed on all such aggregates.
PART IV
SUMMARY:
THE CONNECTION BETWEEN PROBABILITY, IRREVERSIBILITY, ENTROPY AND THE SECOND LAW
[SECTION A]
(1) Prerequisites and Conditions Necessary for the Application of the Theory of Probabilities