Abstract
We consider the additional entropy production (EP) incurred by a fixed quantum or classical process on some initial state , 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 ,” has a universal information-theoretic form: it is given by the contraction of the relative entropy between and the least-dissipative initial state 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.
- Received 9 March 2021
- Revised 27 September 2021
- Accepted 28 September 2021
DOI:https://doi.org/10.1103/PhysRevE.104.054107
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