Operational Thermodynamics from Purity (extended abstract)

Abstract

This is an extended abstract based on the preprint arXiv:1608.04459. 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 purity as a fundamental ingredient for every sensible theory of thermodynamics. Indeed, in physical theories satisfying these axioms, called sharp theories with purification, every mixed state can be modelled as the marginal of a pure entangled state, and every unsharp measurement can be modelled as a sharp measurement on a composite system. We show that these theories support a well-behaved notion of entropy and of Gibbs states, by which one can derive Landauer's principle. We show that in sharp theories with purification some bipartite states can have negative conditional entropy, and we construct an operational protocol exploiting this feature to overcome Landauer's principle