Abstract
Exact results about the nonequilibrium thermodynamics of open quantum systems at arbitrary timescales are obtained by considering all possible variations of initial conditions of a system. First we obtain a quantum-information theoretic equality for entropy production, valid for an arbitrary initial joint state of system and environment. For any finite-time process with a fixed initial environment, we then show that the system's loss of distinction-relative to the minimally dissipative state-exactly quantifies its thermodynamic dissipation. The quantum component of this dissipation is the change in coherence relative to the minimally dissipative state. Implications for quantum state preparation and local control are explored. For nonunitary processes-like the preparation of any particular quantum state-we find that mismatched expectations lead to divergent dissipation as the actual initial state becomes orthogonal to the anticipated one.
Highlights
Much recent progress extends Landauer’s principle to the quantum regime—affirming that quantum information is physical [1,2,3,4,5]
Our approach involves developing a framework to determine how initial conditions of system and environment affect entropy production in general for any finite-time quantum process. This leads to an information-theoretic decomposition of entropy production [see Eq (7) below], which shows that entropy production is the change in total correlation among system and baths plus the changes in nonequilibrium addition to free energy of each thermodynamic bath
When a system begins in any state other than the minimally dissipative initial state, the extra dissipation is exactly the contraction of the quantum relative entropy between them over the duration of the control protocol—their loss of distinguishability
Summary
Much recent progress extends Landauer’s principle to the quantum regime—affirming that quantum information is physical [1,2,3,4,5]. Our approach involves developing a framework to determine how initial conditions of system and environment affect entropy production in general for any finite-time quantum process This leads to an information-theoretic decomposition of entropy production [see Eq (7) below], which shows that entropy production is the change in total correlation among system and baths plus the changes in nonequilibrium addition to free energy of each thermodynamic bath. Of open quantum systems [7], including fluctuation relations [8,9,10,11,12,13,14,15,16,17,18], a previous information-theoretic decomposition of entropy production [19,20], and single-shot results that can be derived from these [21,22] These nonequilibrium equalities subsume the inequality of the Second Law of thermodynamics, and they guide the understanding of farfrom-equilibrium phenomena. Equation (5) has been used to explore entropy production even in the case of arbitrarily small baths [19,28]
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