Subtheory conjecture for sharp theories with purification

A physical theory is said to have a well-behaved thermodynamics when its thermodynamic structure satisfies the relevant well-behavedness requirements. Subtheory conjecture. Every theory with a well-behaved thermodynamics must be a subtheory of a sharp theory with purification. Sharp theories with purification are the proposed axiomatic setting for statistical mechanics, encompassing quantum theories with complex and real amplitudes and certain extensions of classical probability theory. The source gives no evidence that this conjecture has been resolved.