Extreme Fisher Information, Nonequilibrium Thermodynamics and Reciprocity Relations

In employing MaxEnt, a crucial role is assigned to the reciprocity relations that relate the quantifier to be extremized (Shannon’s entropy S), the Lagrange multipliers that arise during the variational process, and the expectation values that constitute the a priori input information. We review here just how these ingredients relate to each other when the information quantifier S is replaced by Fisher’s information measure I. The connection of these proceedings with thermodynamics constitute our physical background.