Entropy Evolution Under Admissible Dynamics

This paper examines the evolution of admissibility entropy under admissible dynamics. Admissibility entropy was previously defined as a scalar quantity on admissible-closed sets by counting admissible refinements. Here, an admissible evolution of closed sets is defined by composing the underlying flow with the admissibility operator, and the resulting entropy behavior along admissible trajectories is analyzed. It is shown that admissibility entropy may be non-increasing, non-decreasing, or invariant in time, depending on the order relations induced by admissibility along the trajectory. These behaviors are classified structurally and do not rely on thermodynamic assumptions, irreversibility, or physical interpretation. No universal entropy law is asserted. This work continues an admissibility-based framework by establishing entropy dynamics as a consequence of admissibility-induced structure, prior to any application or physical specialization.