Stochastic thermodynamics of Fisher information

TL;DR

This paper explores the stochastic thermodynamics of Fisher information, analyzing its fluctuations, dependence on initial conditions, and impact on thermodynamic quantities like work and entropy.

Contribution

It introduces a framework for understanding Fisher information fluctuations and their thermodynamic implications under different initial conditions.

Findings

Average FI depends on initial conditions and system path.

Fisher information influences irreversible work and entropy.

FI fluctuations follow a parastatistics pattern.

Abstract

In this paper, we investigate the stochastic thermodynamics of Fisher information (FI), meaning we characterize both the \textit{fluctuations} of FI, introducing a parastatistics of that quantity, and thermodynamic quantities. We introduce two initial conditions: an equilibrium initial condition and a minimum entropy initial condition, both under a protocol that drives the system to equilibrium. Its results indicate a dependence of the average FI on both the initial condition and path taken. Furthermore, the results point the chosen parameter directly affects the FI of thermodynamic quantities such as irreversible work and entropy, along with fluctuations of a stochastic FI. Last, we assess the further role of FI of the distribution of thermal quantities within the context of thermostatistical inequalities.