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.