of high entropy. We may simplify our proof by considering the return passage from
to
to in part occur isothermally and in part isentropically; then external agencies must produce work and absorb an equivalent amount of heat.
[16]With the help of the preceding footnote this argument can be followed through in detail for each of the cases enumerated on [p. 31]; only the complicated case of diffusion presents any difficulty.
(4) Convenience of the Fiction, the Reversible Processes
A reversible process we have declared to be only an ideal case, a convenient and fruitful fiction which we can imagine by eliminating from an irreversible process one or more of its inevitable accompaniments like friction or heat conduction. But reversible (as well as irreversible) processes have common features. "They resemble each other more than they do any one irreversible process. This is evident from an examination of the differential equations which control them; the differential with respect to time is always of an even order, because the essential sign of time can be reversed. Then too they (in whatever domain of physics they may lie) have the common property that the Principle of Least Action can represent all of them completely and uniquely determines the sequence of their events." They are useful for theoretical demonstration and for the study of conditions of equilibrium.
There is a certain, limited, incomplete sense in which we say that we can change from one state of equilibrium to another in a reversible manner. For example, we can, considering only the one converting (or intermediate) body, effect said change by a successive use of isentropic and isothermal change. But this ignores all but one of the participating bodies and this is not permissible if we strictly adhere to the true definition of complete reversible action.
We must remember too that no other universal measure of irreversibility exists than entropy. "Dissipation" of energy has been put forward as such a measure, but we know already of two irreversible cases where there is no change of energy, namely, diffusion and expansion of a gas into a vacuum. [Unavailable, distributed, scattered energy are terms which could be used here, free from all objection.]