Dissipated Work in Nonequilibrium Process and Relative Fisher Information

Abstract

The relative Fisher information is less acknowledged by the general physics compared with the relative entropy (Kullback–Leibler divergence). We recapitulate the author's recent work on its use in the consideration of an evaluation of the gradient of the dissipated work in phase space during nonequilibrium operations from the viewpoint of information theory. The probability distributions in thermal equilibrium corresponding to the forward and backward processes are assumed. A profound constraint is found to be obtained thanks to the logarithmic Sobolev inequality. We see that both the relative entropy and the Fisher information of the canonical distributions provide a possible lower bound for the phase space structure of the associated process.