Non-identifiability of first-exit mechanisms under state-only observation

An independently characterized undriven Markov model may predict first exit from an admissible region at a time that differs from the observed exit. We ask what such a discrepancy identifies about the underlying physical mechanism. For finite-state continuous-time Markov chains, three distinct model classes can shift first exit: direct addition of transition channels while the nominal channels remain intact, modification of the nominal transition rates, and motion of the admissibility boundary. We prove a constructive non-identifiability theorem. Every direct added-channel realization has a modified-kinetics twin with the same aggregate generator and therefore the same probability measure on complete unmarked state trajectories. No statistic constructed solely from the unmarked state history, including fixed-domain first-exit statistics, distinguishes the pair. Boundary motion supplies a third ambiguity because it can alter exit behavior without changing the state law. Established entropy-production and temporal-viability inequalities then provide conditional model-class tests. For direct added-channel dynamics, an immediate uniformization of the Horowitz–Zhou–England bound gives a positive dissipation floor over any compact admissible region separated from equilibrium. A two-state example has identical observed state-path laws but steady physical entropy-production rates of 3.791 and 0 in the two physical realizations.