Two constructive proofs on d-majorization and thermo-majorization

Abstract

Two constructive proofs on d-majorization and thermo-majorization are provided. In the first part, we present a diagrammatic proof of the equivalence between d-majorization and the existence of a proper stochastic matrix. We explicitly construct the desired stochastic matrix by using a graphical argument. In the second part, we present a constructive proof of the equivalence between the Gibbs-preserving map and thermal operation in classical systems. We construct the desired thermal operation and a heat bath which emulates any Gibbs-preserving map with an arbitrary accuracy.

22 pages, 9 figures

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• Catalysis in Action via Elementary Thermal Operations
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• Exploring the Limits of Controlled Markovian Quantum Dynamics with Thermal Resources
• A hierarchy of thermal processes collapses under catalysis
• The Thermomajorization Polytope and Its Degeneracies
• Quantum thermodynamics with coherence: Covariant Gibbs-preserving operation is characterized by the free energy
• Thermodynamic state convertibility is determined by qubit cooling and heating
• Universality and classification of elementary thermal operations
• Relative volume of comparable pairs under semigroup majorization