“Viability Geometry of Persistence in Irreversible Dynamical Systems: Completeness, Support Rank, and Scalar Infeasibility” The work studies persistence under irreversible dissipative dynamics as a geometric first-exit problem from a constraint-defined operational identity region. For CP-divisible open-system dynamics with faithful stationary state π, the paper proves that cumulative entropy production determines first-exit time if and only if the admissible identity region is radial with respect to the contractive divergence D(·∥π). The manuscript develops three geometric results characterizing persistence support in the non-radial case: the Support Rank Theorem, the Angular Support Penalty, and the Scalar Infeasibility Theorem. An explicit non-radial quantum dynamical semigroup construction is provided together with illustrative multi-constraint dissipative examples.
Dimitri Cerny (2026) studied this question.