Geometric admissibility of identity persistence under entropy-producing open-system dynamics

We analyze the geometric content of thermodynamic persistence constraints in Markovian open quantum systems. Using standard results for quantum dynamical semigroups, including monotonicity of quantum relative entropy under completely positive trace-preserving (CPTP) maps and Spohn’s theorem, persistence is formulated as a first-exit problem from an operationally defined identity region in state space. In CP-divisible dynamics, cumulative entropy production yields a necessary admissibility bound for persistence. We show by explicit construction that two Markovian protocols can produce identical cumulative entropy production at a fixed horizon time yet exhibit different first-exit times, reflecting the nonradial geometry of operational identity regions. The analysis introduces no new dynamical laws and instead isolates a structural admissibility constraint implicit in contractive open-system evolution.