Seems like the main additional source of complexity is that each interface has its own local constraint, and the local constraints are coupled with each other (but lower-dimensional than parameters themselves); whereas regular statmech usually have subsystems sharing the same global constraints (different parts of a room of ideal gas are independent given the same pressure/temperature etc)
To recover the regular statmech picture, suppose that the local constraints have some shared/redundant information with each other: Ideally we’d like to isolate that redundant/shared information into a global constraint that all interfaces has access to, and we’d want the interfaces to be independent given the global constraint. For that we need something like relational completeness, where indexical information is encoded within the interfaces themselves, while the global constraint is shared across interfaces.
Seems like the main additional source of complexity is that each interface has its own local constraint, and the local constraints are coupled with each other (but lower-dimensional than parameters themselves); whereas regular statmech usually have subsystems sharing the same global constraints (different parts of a room of ideal gas are independent given the same pressure/temperature etc)
To recover the regular statmech picture, suppose that the local constraints have some shared/redundant information with each other: Ideally we’d like to isolate that redundant/shared information into a global constraint that all interfaces has access to, and we’d want the interfaces to be independent given the global constraint. For that we need something like relational completeness, where indexical information is encoded within the interfaces themselves, while the global constraint is shared across interfaces.