2016/08/16 by Giulio Chiribella, Chiribella, Giulio, Carlo Maria Scandolo +1 · 1 citation
Computer Science · Physics and Astronomy · #Computability, Logic, AI Algorithms #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.1608.04459
openalex publication_date 2016/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose four information-theoretic axioms for the foundations of statistical mechanics in general physical theories. The axioms---Causality, Purity Preservation, Pure Sharpness, and Purification---identify a class of theories where every mixed state can be modelled as the marginal of a pure entangled state and where every unsharp measurement can be modelled as a sharp measurement on a composite system. This class of theories, called sharp theories with purification, includes quantum theory both with complex and real amplitudes, as well as a suitable extension of classical probability theory where classical systems can be entangled with other, non-classical systems. Theories satisfying our axioms support well-behaved notions of majorization, entropy, and Gibbs states, allowing for an information-theoretic derivation of Landauer's principle. We conjecture that every theory admitting a sensible thermodynamics must be extendable to a sharp theory with purification.