Entropy quantifies informational dispersion in stochastic systems, whereas Fisher information
measures local sensitivity to parametric perturbations. This paper introduces the Information Entropy
Performance Indicator (IEPI), a discrete information-theoretic framework that jointly characterises
uncertainty 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, yielding
a responsiveness-induced entropy floor and enabling precise viability criteria. IEPI thus provides a
mathematically rigorous basis for steering adaptive processes within defined informational limits.
