Quantum thermodynamics of correlated-catalytic state conversion at small-scale

Abstract

The class of possible thermodynamic conversions can be extended by introducing an auxiliary system called catalyst, which assists state conversion while remaining its own state unchanged. We reveal a complete characterization of catalytic state conversion in quantum and single-shot thermodynamics by allowing an infinitesimal correlation between the system and the catalyst. Specifically, we prove that a single thermodynamic potential, which provides the necessary and sufficient condition for the correlated-catalytic state conversion, is given by the standard nonequilibrium free energy defined with the Kullback-Leibler divergence. This resolves the conjecture raised by Wilming, Gallego, and Eisert [Entropy 19, 241 (2017)] and by Lostaglio and Muller [Phys. Rev. Lett. 123, 020403 (2019)] in positive. Moreover, we show that, with the aid of the work storage, any quantum state can be converted into another one by paying the work cost equal to the difference of the nonequilibrium free energy. Our result would serve as a step towards establishing resource theories of catalytic state conversion in the fully quantum regime.

15 pages, 3 figures

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• Fundamental Limits on Correlated Catalytic State Transformations
• Operational definition of the temperature of a quantum state
• Is there a finite complete set of monotones in any quantum resource theory?
• Continuous thermomajorization and a complete set of laws for Markovian thermal processes
• Fundamental limits on anomalous energy flows in correlated quantum systems
• Correlations in typicality and an affirmative solution to the exact catalytic entropy conjecture
• Catalytic leverage of correlations and mitigation of dissipation in Information erasure
• Arbitrary Amplification of Quantum Coherence in Asymptotic and Catalytic Transformation
• Catalytic Transformations in Coherence Theory
• Catalysis in Action via Elementary Thermal Operations
• Catalytic advantage in Otto-like two-stroke quantum engines
• Covariant catalysis requires correlations and good quantum reference frames degrade little
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• Coherence manipulation in asymmetry and thermodynamics
• Entanglement catalysis for quantum states and noisy channels
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• Catalytic and asymptotic equivalence for quantum entanglement
• Quantum catalysis in cavity quantum electrodynamics
• Complete Characterization of Entanglement Embezzlement
• Catalytic Gaussian thermal operations
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• Second Law of Entanglement Manipulation with Entanglement Battery
• Catalytic enhancement in the performance of the microscopic two-stroke heat engine
• Teleportation with Embezzling Catalysts
• Gibbs-preserving operations requiring infinite amount of quantum coherence
• Black Box Work Extraction and Composite Hypothesis Testing
• Quantum thermodynamics with coherence: Covariant Gibbs-preserving operation is characterized by the free energy
• Communication with Quantum Catalysts
• Conditional quantum thermometry -- enhancing precision by measuring less
• Catalytic transformations with finite-size environments: applications to cooling and thermometry
• Correlational Resource Theory of Catalytic Quantum Randomness under Conservation Law
• Experimental Catalytic Amplification of Asymmetry
• Unlocking inaccessible performance of the quantum refrigerator with catalysts
• Universal work extraction in quantum thermodynamics
• Notes on quantum coherence with l_1-norm and convex-roof l_-norm
• Thermal operations from informational equilibrium
• Finite-size catalysis in quantum resource theories
• Advantage of flexible catalysis for entanglement and quantum thermodynamics