Informational steady-states and conditional entropy production in continuously monitored systems

TL;DR

This paper develops a unified thermodynamic framework for continuously monitored systems, linking entropy production to information measures and identifying conditions for informational steady-states.

Contribution

It introduces a formalism connecting entropy production and information flow, revealing conditions for informational steady-states in monitored open systems.

Findings

Conditional and unconditional entropy production are related by the Holevo quantity.

Existence of informational steady-states depends on continuous information acquisition.

Framework is demonstrated through multiple illustrative examples.

Abstract

We put forth a unifying formalism for the description of the thermodynamics of continuously monitored systems, where measurements are only performed on the environment connected to a system. We show, in particular, that the conditional and unconditional entropy production, which quantify the degree of irreversibility of the open system's dynamics, are related to each other by the Holevo quantity. This, in turn, can be further split into an information gain rate and loss rate, which provide conditions for the existence of informational steady-states (ISSs), i.e. stationary states of a conditional dynamics that are maintained owing to the unbroken acquisition of information. We illustrate the applicability of our framework through several examples.