• Open Access

Informational Steady States and Conditional Entropy Production in Continuously Monitored Systems

Gabriel T. Landi, Mauro Paternostro, and Alessio Belenchia
PRX Quantum 3, 010303 – Published 5 January 2022

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.

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  • 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)

Statistical Physics & ThermodynamicsQuantum Information, Science & Technology

Authors & Affiliations

Gabriel T. Landi1,*, Mauro Paternostro2, and Alessio Belenchia3,2

  • 1Instituto de Física da Universidade de São Paulo, São Paulo 05314-970, Brazil
  • 2Centre for Theoretical Atomic, Molecular, and Optical Physics, School of Mathematics and Physics, Queens University, Belfast BT7 1NN, United Kingdom
  • 3Institut für Theoretische Physik, Eberhard-Karls-Universität Tübingen, Tübingen 72076, Germany

  • *gtlandi@if.usp.br

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.

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See Also

Informational steady states and conditional entropy production in continuously monitored systems: The case of Gaussian systems

Alessio Belenchia, Mauro Paternostro, and Gabriel T. Landi
Phys. Rev. A 105, 022213 (2022)

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Vol. 3, Iss. 1 — January - March 2022

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It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

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