Fisher information and thermodynamics' 1st. law

A. Plastino, A. R. Plastino, B. H. Soffer

Published 2005-09-27, updated 2005-09-28Version 2

It was recently shown, starting from first principles, that thermodynamics' first law (TFL) can be microscopically obtained without need of invoking the adiabatic theorem (AT) [Physica A, {\bf 356}, 167 (2005)]. We show here that a TFL can also be found for Fisher's information measure, following a similar procedure. Further, it is proved that enforcing the Fisher-first law requirements in a process in which the probability distribution is infinitesimally varied is equivalent to minimizing Fisher's information measure subject to appropriate constraints.