It is to Clausius that was reserved the credit of rediscovering the principle, and of enunciating it in language conformable to the new doctrines, while giving it a much greater generality.  The postulate arrived at by experimental induction, and which must be admitted without demonstration, is, according to Clausius, that in a series of transformations in which the final is identical with the initial stage, it is impossible for heat to pass from a colder to a warmer body unless some other accessory phenomenon occurs at the same time.

Still more correctly, perhaps, an enunciation can be given of the postulate which, in the main, is analogous, by saying:  A heat motor, which after a series of transformations returns to its initial state, can only furnish work if there exist at least two sources of heat, and if a certain quantity of heat is given to one of the sources, which can never be the hotter of the two.  By the expression “source of heat,” we mean a body exterior to the system and capable of furnishing or withdrawing heat from it.

Starting with this principle, we arrive, as does Clausius, at the demonstration that the output of a reversible machine working between two given temperatures is greater than that of any non-reversible engine, and that it is the same for all reversible machines working between these two temperatures.

This is the very proposition of Carnot; but the proposition thus stated, while very useful for the theory of engines, does not yet present any very general interest.  Clausius, however, drew from it much more important consequences.  First, he showed that the principle conduces to the definition of an absolute scale of temperature; and then he was brought face to face with a new notion which allows a strong light to be thrown on the questions of physical equilibrium.  I refer to entropy.

It is still rather difficult to strip entirely this very important notion of all analytical adornment.  Many physicists hesitate to utilize it, and even look upon it with some distrust, because they see in it a purely mathematical function without any definite physical meaning.  Perhaps they are here unduly severe, since they often admit too easily the objective existence of quantities which they cannot define.  Thus, for instance, it is usual almost every day to speak of the heat possessed by a body.  Yet no body in reality possesses a definite quantity of heat even relatively to any initial state; since starting from this point of departure, the quantities of heat it may have gained or lost vary with the road taken and even with the means employed to follow it.  These expressions of heat gained or lost are, moreover, themselves evidently incorrect, for heat can no longer be considered as a sort of fluid passing from one body to another.

The real reason which makes entropy somewhat mysterious is that this magnitude does not fall directly under the ken of any of our senses; but it possesses the true characteristic of a concrete physical magnitude, since it is, in principle at least, measurable.  Various authors of thermodynamical researches, amongst whom M. Mouret should be particularly mentioned, have endeavoured to place this characteristic in evidence.