We study the informational underpinnings of thermodynamics and statistical
mechanics, using an abstract framework, general probabilistic theories, capable
of describing arbitrary physical theories. This allows one to abstract the
informational content of a theory from the concrete details of its formalism.
In this framework, we extend the treatment of microcanonical thermodynamics,
namely the thermodynamics of systems with a well-defined energy, beyond the
known cases of classical and quantum theory, formulating two necessary