Relations between entropy rate, entropy production and information geometry in linear stochastic systems

TL;DR

This paper explores the connections between information geometry, entropy measures, and thermodynamics in linear stochastic systems, proposing new methods for event detection and control based on these concepts.

Contribution

It introduces a novel framework linking information rate, entropy production, and entropy geometry in linear stochastic processes, with practical applications in detection and control.

Findings

Exact calculations of information rate, entropy rate, and entropy production for linear stochastic systems.

Development of entropic correlation coefficients for abrupt event detection.

Design of thermodynamic control policies using information geometric cost functions.

Abstract

In this work, we investigate the relation between the concept of ``information rate'', an information geometric method for measuring the speed of the time evolution of the statistical states of a stochastic process, and stochastic thermodynamics quantities like entropy rate and entropy production. Then, we propose the application of entropy rate and entropy production to different practical applications such as abrupt event detection, correlation analysis, and control engineering. Specifically, by utilising the Fokker-Planck equation of multi-variable linear stochastic processes described by Langevin equations, we calculate the exact value for information rate, entropy rate, and entropy production and derive various inequalities among them. Inspired by classical correlation coefficients and control techniques, we create entropic-informed correlation coefficients as abrupt event detection methods and information geometric cost functions as optimal thermodynamic control policies, respectively. The methods are analysed via the numerical simulations of common prototypical systems.