Entropy and Fisher Information in Process Viability: The IEPI Framework

Entropy quantifies informational dispersion in stochastic systems, whereas Fisher informationmeasures local sensitivity to parametric perturbations. This paper introduces the Information EntropyPerformance Indicator (IEPI), a discrete information-theoretic framework that jointly characterisesuncertainty and responsiveness to assess the viability of stochastic processes. A functional entropy range[H_min^*,H_max^* ] defines a bounded regime between deterministic rigidity and stochastic instability.Analytical results establish a formal coupling between Shannon entropy and Fisher information, yieldinga responsiveness-induced entropy floor and enabling precise viability criteria. IEPI thus provides amathematically rigorous basis for steering adaptive processes within defined informational limits.