Recovery of the second law in fully quantum thermodynamics

• URL: http://arxiv.org/abs/2510.05642v1
• Date: Tue, 07 Oct 2025 07:42:38 GMT
• Title: Recovery of the second law in fully quantum thermodynamics
• Authors: Naoto Shiraishi, Ryuji Takagi,
• Abstract summary: We show that the state convertibility under thermal operations is fully characterized by the second law of thermodynamics.<n>We prove that whether a quantum state with quantum coherence is convertible to another by a thermal operation with a correlated catalyst is completely determined by the free energy ordering.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum thermodynamics investigates how robust the second law of thermodynamics serves as the unique fundamental law in the small quantum world. To tackle this problem, the quantum coherence constitutes a major difficulty of investigations, which provides severe constraints hindering the recovery of a single thermodynamic potential. Here we solve this long-standing problem of quantum information theory by revealing that the state convertibility under thermal operations is fully characterized by the second law of thermodynamics. Specifically, we prove that whether a quantum state with quantum coherence is convertible to another by a thermal operation with a correlated catalyst is completely determined by the free energy ordering. Unlike previous attempts, our setting does not resort to any additional external coherent assist, providing a faithful operational characterization of thermodynamic state transformation.

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