Information-thermodynamic cost of stabilized persistence under irreversible dynamics

Persistence beyond the passive first-exit time imposes a thermodynamic constraint: the entropy production required to maintain distinguishability cannot be confined to a coarse-grained subsystem but must be exported to auxiliary degrees of freedom. In the information-assisted stabilization regime, this constraint appears as a lower bound on exported entropy flow in terms of the information acquired for correction. Finite-resolution identity relative to a reference baseline induces a distinguishability margin and a corresponding passive first-exit time under irreversible dynamics. Maintaining persistence beyond this limit therefore requires continuous external support that offsets contractive drift, and the controller-resolved second law fixes where the associated thermodynamic cost must appear. This establishes a structural localization constraint: persistence beyond what the internal dynamics sustain entails exported irreversibility, and provides a directly testable diagnostic criterion: if observed persistence exceeds the passive first-exit time predicted from independently characterized internal dynamics, the supporting processes must lie outside the chosen system boundary. This result is complementary to Landauer’s principle: while Landauer bounds the thermodynamic cost of destroying distinguishability, the present result bounds the cost of maintaining it against irreversible contraction. A minimal four-state bipartite Markov model illustrates how stabilization extends persistence while generating the required entropy flow. When stabilization fails, identity loss occurs as an irreversible boundary-crossing event.