Physical Interpretation of Admissibility Entropy

This paper examines the conditions under which admissibility entropy may be interpreted as a physical entropy. Admissibility entropy was previously defined as a structural quantity associated with admissible-closed sets and shown to admit monotone evolution under admissible dynamics. Here, observable quantities are introduced as projections of the underlying state space, and an entropy induced on observable outcomes is defined. Under minimal assumptions, it is shown that observable entropy is bounded above by admissibility entropy. A conditional compatibility result is given relating admissibility entropy to thermodynamic entropy, without asserting that physical systems satisfy the stated assumptions. No physical laws, experimental claims, or dynamical postulates are introduced. This work establishes a controlled bridge between admissibility-based structure and physical interpretation, preserving the structural character of the framework while identifying the requirements under which physical meaning may be coherently assigned.