Thermodynamics and the structure of quantum theory

Abstract

Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some regimes of physics? Here we address these questions by studying how compatibility with thermodynamics constrains the structure of quantum theory. We employ two postulates that any probabilistic theory with reasonable thermodynamic behavior should arguably satisfy. In the framework of generalized probabilistic theories, we show that these postulates already imply important aspects of quantum theory, like self-duality and analogues of projective measurements, subspaces and eigenvalues. However, they may still admit a class of theories beyond quantum mechanics. Using a thought experiment by von Neumann, we show that these theories admit a consistent thermodynamic notion of entropy, and prove that the second law holds for projective measurements and mixing procedures. Furthermore, we study additional entropy-like quantities based on measurement probabilities and convex decomposition probabilities, and uncover a relation between one of these quantities and Sorkin's notion of higher-order interference.

19+8 pages, 5 figures. See also the related work by Chiribella and Scandolo in arXiv:1608.04459 and arXiv:1608.04460. v2: close to published version

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• Universal validity of the second law of information thermodynamics
• Universal structure of objective states in all fundamental causal theories
• Preparation Uncertainty Implies Measurement Uncertainty in a Class of Generalized Probabilistic Theories
• Derivation of quantum theory with superselection rules
• Von Neumann's information engine without the spectral theorem
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• Entropy of mixing exists only for classical and quantum-like theories among the regular polygon theories
• A computer scientist's reconstruction of quantum theory
• Entropic Uncertainty Relations in a Class of Generalized Probabilistic Theories
• Density Hypercubes, Higher Order Interference and Hyper-Decoherence: a Categorical Approach
• Extending Resource Monotones using Kan Extensions
• Compositional Thermostatics
• One-shot and asymptotic classical capacity in general physical theories
• The thermodynamics of readout devices and semiclassical gravity
• Spacetime symmetries and the qubit Bloch ball: a physical derivation of finite dimensional quantum theory and the number of spatial dimensions
• From Thermodynamic Sufficiency to Information Causality
• Can QBism exist without Q? Morphophoric measurements in generalised probabilistic theories
• Does Quantum Mechanics Breed Larger, More Intricate Quantum Theories? The Case for Experience-Centric Quantum Theory and the Interactome of Quantum Theories