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

• URL: http://arxiv.org/abs/2103.05734v4
• Date: Mon, 6 Jun 2022 02:08:22 GMT
• Title: Dependence of integrated, instantaneous, and fluctuating entropy production on the initial state in quantum and classical processes
• Authors: Artemy Kolchinsky, David H. Wolpert
• Abstract summary: We consider the additional entropy production (EP) incurred by a fixed quantum or classical process on some initial state $rho$. We show that this additional EP, which we term the "mismatch cost of $rho$", has a universal information-theoretic form.
• Score: 2.5454615592832917
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the additional entropy production (EP) incurred by a fixed quantum or classical process on some initial state $\rho$, 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 $\rho$", has a universal information-theoretic form: it is given by the contraction of the relative entropy between $\rho$ and the least-dissipative initial state $\varphi$ 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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