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arXiv:1805.09564 · Fundamental theories of physics

Resource Theory of Quantum Thermodynamics: Thermal Operations and Second Laws

Nelly Huei Ying Ng, Mischa P. Woods

Published Jan 1, 2018• 35 citations
arXivHTMLPDF
DOI
10.1007/978-3-319-99046-0_26

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The resource theory of thermal operations explains the state transformations that are possible in a very specific thermodynamic setting: there is only one thermal bath, auxiliary systems can only be in the corresponding thermal state (free states), and the interaction must commute with the free Hamiltonian (free operation). In this paper we study the mildest deviation: the reservoir particles are subject to inhomogeneities, either in the local temperature (introducing resource states) or in the local Hamiltonian (generating a resource operation). For small inhomogeneities, the two models generate the same channel and thus the same state transformations. However, their thermodynamics is significantly different when it comes to work generation or to the interpretation of the ``second laws of thermal operations.''
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.