Neither must we conceal from ourselves that the definition supposes, for a given body, the possibility of passing from one state to another by a reversible transformation.  Reversibility is an ideal and extreme case which cannot be realized, but which can be approximately attained in many circumstances.  So with gases and with perfectly elastic bodies, we effect sensibly reversible transformations, and changes of physical state are practically reversible.  The discoveries of Sainte-Claire Deville have brought many chemical phenomena into a similar category, and reactions such as solution, which used to be formerly the type of an irreversible phenomenon, may now often be effected by sensibly reversible means.  Be that as it may, when once the definition is admitted, we arrive, by taking as a basis the principles set forth at the inception, at the demonstration of the celebrated theorem of Clausius:  The entropy of a thermally isolated system continues to increase incessantly.

It is very evident that the theorem can only be worth applying in cases where the entropy can be exactly defined; but, even when thus limited, the field still remains vast, and the harvest which we can there reap is very abundant.

Entropy appears, then, as a magnitude measuring in a certain way the evolution of a system, or, at least, as giving the direction of this evolution.  This very important consequence certainly did not escape Clausius, since the very name of entropy, which he chose to designate this magnitude, itself signifies evolution.  We have succeeded in defining this entropy by demonstrating, as has been said, a certain number of propositions which spring from the postulate of Clausius; it is, therefore, natural to suppose that this postulate itself contains in potentia the very idea of a necessary evolution of physical systems.  But as it was first enunciated, it contains it in a deeply hidden way.

No doubt we should make the principle of Carnot appear in an interesting light by endeavouring to disengage this fundamental idea, and by placing it, as it were, in large letters.  Just as, in elementary geometry, we can replace the postulate of Euclid by other equivalent propositions, so the postulate of thermodynamics is not necessarily fixed, and it is instructive to try to give it the most general and suggestive character.

MM.  Perrin and Langevin have made a successful attempt in this direction.  M. Perrin enunciates the following principle:  An isolated system never passes twice through the same state.  In this form, the principle affirms that there exists a necessary order in the succession of two phenomena; that evolution takes place in a determined direction.  If you prefer it, it may be thus stated:  Of two converse transformations unaccompanied by any external effect, one only is possible.  For instance, two gases may diffuse themselves one in the other in constant volume, but they could not conversely separate themselves spontaneously.