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

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.

Automated summary

In this work, we investigate the relation between 'information rate' and stochastic thermodynamics quantities such as entropy rate and entropy production. We propose the application of entropy rate and entropy production to practical applications including abrupt event detection, correlation analysis, and control engineering. Utilizing the Fokker-Planck equation, we calculate exact values for information rate, entropy rate, and entropy production and derive various inequalities among them. We also create entropic-informed correlation coefficients and information geometric cost functions for abrupt event detection and optimal thermodynamic control policies respectively.