On the Equivalence and Optimality of Transformations of Diffusive Systems

In this paper we introduce, inspired by Clausius and developing the ideas of [11], the concept of equivalence of transformations in non equilibrium theory of diffusive systems within the framework of macroscopic fluctuation theory. Besides providing a new proof of a formula derived in [3, 4], which is the basis of the equivalence, we show that equivalent quasistatic transformations can be distinguished in finite terms, by the renormalized work introduced in [1,2,3,4]. This allows us to tackle the problem of determining the optimal quasistatic transformation among the equivalent ones.