This preprint develops a theoretical framework for local access and reconstruction of global compatibility in spectral systems, suggesting implications for quantum measures.
Key Points
The aim is to establish a theory of spectral closure systems that facilitates local access to global compatibility through entropic measures and reconstruction techniques.
Developed an operator-algebraic framework for local closure and access maps.
Analyzed local charts and obstructions using compactness and inverse system extendability.
Classified entropy measures and independent theorems in the context of quantum compatibility.
Recovery of local charts is exact on the sufficiency sector, with implications for Petz recovery and conditioning.
Found that off the sufficiency sector, totalization incurs an exact entropy cost, indicating a fundamental trade-off.
Established a logarithmic Sobolev inequality for temporal modules, applicable to modular cocycles.