Entropy and reversible catalysis

Abstract

I show that non-decreasing entropy provides a necessary and sufficient condition to convert the state of a physical system into a different state by a reversible transformation that acts on the system of interest and a further "catalyst" whose state has to remain invariant exactly in the transition. This statement is proven both in the case of finite-dimensional quantum mechanics, where von~Neumann entropy is the relevant entropy, and in the case of systems whose states are described by probability distributions on finite sample spaces, where Shannon entropy is the relevant entropy. The results give an affirmative resolution to the (approximate) "catalytic entropy conjecture" introduced by Boes et al. [PRL 122, 210402 (2019)]. They provide a complete single-shot characterization without external randomness of von Neumann entropy and Shannon entropy. I also compare the results to the setting of phenomenological thermodynamics and show how they can be used to obtain a quantitative single-shot characterization of Gibbs states in quantum statistical mechanics.

5+5 pages; 3+1 figures. Comments welcome!; v2: added comparison to thermodynamics and application to quantum statistical mechanics, expanded appendix, minor corrections, close to published version

References in corpus (9)

• Reference frames, superselection rules, and quantum information
• Extending Noether's theorem by quantifying the asymmetry of quantum states
• A Sharp Fannes-type Inequality for the von Neumann Entropy
• Necessary and Sufficient Conditions for the Trumping Relation
• Catalytic Conversion Probabilities for Bipartite Pure States
• Catalytic quantum teleportation and beyond
• Quantum thermodynamics of correlated-catalytic state conversion at small-scale
• Catalytic Transformations of Pure Entangled States
• Inequalities that Collectively Completely Characterize the Catalytic Majorization Relation

Cited by in corpus (17)

• Catalytic quantum teleportation and beyond
• Catalytic Transformations of Pure Entangled States
• Catalysis of entanglement and other quantum resources
• Correlation in Catalysts Enables Arbitrary Manipulation of Quantum Coherence
• 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?
• Correlations in typicality and an affirmative solution to the exact catalytic entropy conjecture
• The refined quantum extremal surface prescription from the asymptotic equipartition property
• Catalysis in Action via Elementary Thermal Operations
• Covariant catalysis requires correlations and good quantum reference frames degrade little
• Entanglement catalysis for quantum states and noisy channels
• Thermodynamically free quantum measurements
• Transcendental properties of entropy-constrained sets
• Catalytic transformations with finite-size environments: applications to cooling and thermometry
• Correlational Resource Theory of Catalytic Quantum Randomness under Conservation Law
• Hacking Quantum Networks: Extraction and Installation of Quantum Data