Fisher information and thermodynamics' 1st. law

TL;DR

This paper demonstrates that a form of the first law of thermodynamics can be derived from Fisher's information measure, linking thermodynamics principles with information theory without relying on traditional adiabatic assumptions.

Contribution

It introduces a Fisher information-based first law, showing its derivation from first principles and its equivalence to Fisher information minimization under constraints.

Findings

Fisher's information measure obeys a first law similar to thermodynamics.

Enforcing Fisher-first law leads to Fisher information minimization.

Provides a new perspective connecting thermodynamics and information theory.

Abstract

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.