Information-Geometric First-Passage Monitoring of Distributional Stability in Stochastic Systems

Abstract

Runtime monitoring of stochastic systems must distinguish nominal distributional relaxation from regime departure while controlling repeated-test false alarms under explicit validity assumptions. This paper links relative-entropy dissipation, information geometry, and sequential inference in a bounded first-passage monitoring architecture. For reversible Fokker--Planck dynamics, relative entropy to an invariant density is non-increasing; under exogenous forcing, its derivative decomposes into nominal dissipation and an information-space forcing term. The runtime layer uses Gaussian window surrogates, nominal-relative covariance shrinkage, a coordinate-consistent relative precision diagnostic, and randomized conformal ranks aggregated by a mixture power-martingale process. Analytical Ornstein--Uhlenbeck validation gives zero positive nominal Kullback--Leibler increments, forcing-identity residuals below 3.31 x 10^-6, and coordinate-invariance errors at numerical roundoff. On NSL-KDD, the monitor yields 0/100 alarms on internal nominal streams but 63/100 on official test-normal streams; post-change detection is 99.0% for seen and 98.53% for test-only attack types with median one-window delay. On UNSW-NB15, internal-null alarms are 0/100, whereas official test-normal alarms rise to 90/100; post-change detection is 81.33%, with 18.67% pre-change alarms. In these evaluations, calibration transport emerges as a major deployment constraint. No universal benchmark superiority, causal inference, or physical-work interpretation is claimed.