Microcanonical thermodynamics in general physical theories

Abstract

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 theory of microcanonical thermodynamics and the resource theory of pure bipartite entanglement.

21+6 pages, 3 figures, extended framework including general systems with constraints, close to published version. See also the related work by Krumm, Barnum, Barrett, and Mueller on arXiv:1608.04461

References in corpus (10)

• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Quantum coherence, time-translation symmetry and thermodynamics
• A derivation of quantum theory from physical requirements
• A generalized no-broadcasting theorem
• Introduction to the book "Quantum Theory: Informational Foundations and Foils"
• Gibbs-Preserving Maps outperform Thermal Operations in the quantum regime
• Higher-order interference and single-system postulates characterizing quantum theory
• Thermodynamics and the structure of quantum theory
• Dilation of states and processes in operational-probabilistic theories
• Ruling out higher-order interference from purity principles

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