Hidden Markov models for stochastic thermodynamics

TL;DR

This paper applies hidden Markov models to stochastic thermodynamics, providing insights into phase transitions, information value, and causality violations in systems with feedback and measurement errors.

Contribution

It introduces the use of HMM formalism to analyze stochastic thermodynamics, clarifying phase transitions and information effects in feedback systems.

Findings

Measurement noise acts as a control parameter for phase transitions.

Information value peaks at intermediate signal-to-noise ratios.

HMM formalism quantifies performance gains from apparent causality violations.

Abstract

The formalism of state estimation and hidden Markov models (HMMs) can simplify and clarify the discussion of stochastic thermodynamics in the presence of feedback and measurement errors. After reviewing the basic formalism, we use it to shed light on a recent discussion of phase transitions in the optimized response of an information engine, for which measurement noise serves as a control parameter. The HMM formalism also shows that the value of additional information shows a maximum at intermediate signal-to-noise ratios. Finally, we discuss how systems open to information flow can apparently violate causality; the HMM formalism can quantify the performance gains due to such violations.