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Abstract This work presents the Theory of Informational Control (TCI), a mathematical framework in which system dynamics are formulated directly on the space of probability distributions, rather than on physical state variables. Informational states are represented as points in the interior of the probability simplex, arising from measurable partitions or absolutely continuous densities, and system evolution is described through multiplicative, normalization-preserving operators acting on these states. Within TCI, admissible control actions correspond to informational corrections that induce changes of measure and generate a commutative group of diffeomorphisms on the simplex. This structure naturally encompasses Markov dynamics, Bayesian updates, and their compositions as particular cases of a unified operator formalism. Optimal control is defined as the problem of steering an informational state toward a target distribution by minimizing the Kullback–Leibler divergence, which appears as a canonical energy functional on the simplex. Equipping the simplex with the Fisher information metric, the theory yields a well-defined notion of gradient flow, for which the Fisher–KL dynamics admit explicit solutions and satisfy a strict H-theorem. Discrete-time updates, continuous-time limits, and extensions to absolutely continuous probability measures are treated within the same conceptual structure. In this sense, TCI provides a rigorous bridge between information geometry, statistical inference, and control theory, interpreting control as the optimal transport of information under probabilistic constraints. Originality statement This manuscript develops an original and self-contained theoretical framework formulated by Alejandro Cruz-López (Universidad Autónoma Metropolitana – Unidad Iztapalapa). While it builds upon established results in probability theory, information geometry, and information theory, the Theory of Informational Control introduces a novel unifying structure based on multiplicative operators on the probability simplex, their group properties, and their variational characterization via Kullback–Leibler divergence and Fisher geometry. To the author’s knowledge, the systematic integration of Markov processes, Bayesian inference, gradient flows, and control actions within a single operator-theoretic framework acting intrinsically on informational states has not been previously published as a complete theory. Authorship and rights (revised) © Alejandro Cruz-López (2025). All rights reserved. This work is deposited as a preprint in Zenodo for the purpose of establishing authorship, intellectual priority, and a permanent scholarly record. No part of this work may be reproduced, modified, or used for commercial purposes without explicit written permission from the author. Academic citation and non-commercial scholarly use are permitted, provided that proper attribution to the author and the corresponding DOI are included.