Hellmann–Feynman connection for the relative Fisher information

Hellmann-Feynman connection for the relative Fisher information

The (i) reciprocity relations for the relative Fisher information (RFI, hereafter) and (ii) a generalized RFI-Euler theorem, are self-consistently derived from the Hellmann-Feynman theorem. These new reciprocity relations generalize the RFIEuler theorem and constitute the basis for building up a mathematical Legendre transform structure (LTS, hereafter), akin to that of thermodynamics, that und...

Dissipated Work in Nonequilibrium Process and Relative Fisher Information

RELATIVE INFORMATION FUNCTIONAL OF RELATIVE DYNAMICAL SYSTEMS

 In this paper by use of mathematical modeling of an observer [14,15] the notion of relative information functional for relative dynamical systemson compact metric spaces is presented. We extract the information function ofan ergodic dynamical system (X,T) from the relative information of T fromthe view point of observer χX, where X denotes the base space of the system.We also generalize the in...

Relations between Renyi Distance and Fisher Information

In this paper, we first show that Renyi distance between any member of a parametric family and its perturbations, is proportional to its Fisher information. We, then, prove some relations between the Renyi distance of two distributions and the Fisher information of their exponentially twisted family of densities. Finally, we show that the partial ordering of families induced by Renyi dis...

Nonconvexity of the relative entropy for Markov dynamics: a Fisher information approach.

We show via counterexamples that relative entropy between the solution of a Markovian master equation and the steady state is not a convex function of time. We thus disprove the hypotheses that a general evolution principle of thermodynamics based on the decrease of the nonadiabatic entropy production could hold. However, we argue that a large separation of typical decay times is necessary for ...