Dependence of integrated, instantaneous, and fluctuating entropy production on the initial state in quantum and classical processes

Artemy Kolchinsky and David H. Wolpert
Phys. Rev. E 104, 054107 – Published 9 November 2021

Abstract

We consider the additional entropy production (EP) incurred by a fixed quantum or classical process on some initial state ρ, above the minimum EP incurred by the same process on any initial state. We show that this additional EP, which we term the “mismatch cost of ρ,” has a universal information-theoretic form: it is given by the contraction of the relative entropy between ρ and the least-dissipative initial state φ over time. We derive versions of this result for integrated EP incurred over the course of a process, for trajectory-level fluctuating EP, and for instantaneous EP rate. We also show that mismatch cost for fluctuating EP obeys an integral fluctuation theorem. Our results demonstrate a fundamental relationship between thermodynamic irreversibility (generation of EP) and logical irreversibility (inability to know the initial state corresponding to a given final state). We use this relationship to derive quantitative bounds on the thermodynamics of quantum error correction and to propose a thermodynamically operationalized measure of the logical irreversibility of a quantum channel. Our results hold for both finite- and infinite-dimensional systems, and generalize beyond EP to many other thermodynamic costs, including nonadiabatic EP, free-energy loss, and entropy gain.

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  • Received 9 March 2021
  • Revised 27 September 2021
  • Accepted 28 September 2021

DOI:https://doi.org/10.1103/PhysRevE.104.054107

©2021 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsQuantum Information, Science & TechnologyGeneral Physics

Authors & Affiliations

Artemy Kolchinsky* and David H. Wolpert

  • Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA

  • *artemyk@gmail.com
  • Also at Complexity Science Hub, Vienna, and Arizona State University, Tempe, Arizona.

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Issue

Vol. 104, Iss. 5 — November 2021

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