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, 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.
- Received 25 March 2021
- Accepted 10 December 2021
DOI:https://doi.org/10.1103/PRXQuantum.3.010303
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
The second law of thermodynamics quantifies how irreversible is a certain process. However, this law also has a subjective character, associated with our degree of knowledge about the process. Given this knowledge, processes should become more reversible. In quantum systems, quantifying this effect is difficult because measurements become invasive. Here we put forth an overarching framework for treating this effect and constructing a theory of conditional thermodynamics. In particular, our framework also introduces the notion of information steady states. That is, steady states of matter that only exist because measurements are being continually performed.