Entropy is a state function. To prove this assertion, we need to show that the integral
of dS is independent of path. To do so, it is sufficient to prove that the integral of
eqn 3.1 around an arbitrary cycle is zero, for that guarantees that the entropy is the
same at the initial and final states of the system regardless of the path taken between
them (Fig. 3.5). That is, we need to show that