Journal
NEW JOURNAL OF PHYSICS
Volume 19, Issue -, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1367-2630/aa91c7
Keywords
general probabilistic theories; foundations of thermodynamics; microcanonical state; resource theories; quantum entanglement; majorization; information-theoretic axioms
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Funding
- Foundational Questions Institute [FQXiRFP3-1325, FQXi-RFP-1608]
- Canadian Institute for Advanced Research (CIFAR)
- 1000 Youth Fellowship Program of China
- Hong Kong Research Grant Council (RGC) [17326616]
- Engineering and Physical Sciences Research Council (EPSRC) [1652538]
- EPSRC doctoral training grant
- Oxford-Google Deepmind Graduate Scholarship
- Government of Canada through NSERC
- Province of Ontario through MRI
- Engineering and Physical Sciences Research Council [1652538] Funding Source: researchfish
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Microcanonical thermodynamics studies the operations that can be performed on systems with well-defined energy. So far, this approach has been applied to classical and quantum systems. Here we extend it to arbitrary physical theories, proposing two requirements for the development of a general microcanonical framework. We then formulate three resource theories, corresponding to three different sets of basic operations: (i) random reversible operations, resulting from reversible dynamics with fluctuating parameters, (ii) noisy operations, generated by the interaction with ancillas in the microcanonical state, and (iii) unital operations, defined as the operations that preserve the microcanonical state. We focus our attention on a class of physical theories, called sharp theories with purification, where these three sets of operations exhibit remarkable properties. Firstly, each set is contained into the next. Secondly, the convertibility of states by unital operations is completely characterised by a majorisation criterion. Thirdly, the three sets are equivalent in terms of state convertibility if and only if the dynamics allowed by theory satisfy a suitable condition, which we call unrestricted reversibility. Under this condition, we derive a duality between the resource theories of microcanonical thermodynamics and the resource theory of pure bipartite entanglement.
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