Information-theoretic formulation of dynamical systems: causality, modeling, and control

The paper states generalized Fano-type bounds on modeling error (probability and expectation) and a Pinsker-type distributional bound, and motivates maximizing mutual information and minimizing KL divergence for model design. The candidate solution reconstructs these results rigorously: it derives the list-decoding version of Fano’s inequality with an explicit construction of the indicator random variable and the local list size Lε, converts it to the expectation bound via the standard inequality E[Z] ≥ ε P(Z > ε), and proves Pinsker’s inequality in the base-2 convention. These match the paper’s displayed formulas for Pe, E||Q̂−Q̃||, and the Y-quantity bounds, including the KL-to-TV relation. Minor gaps in the paper’s presentation (no proof of the generalized Fano step, loose treatment of Lε and partition geometry, and a slightly imprecise remark about concavity of mutual information) are supplied or clarified by the model. Overall, the claims coincide and are correct; the proofs differ in detail but are consistent with the paper’s statements and intent (Pe bound and expectation bound: 5.12–5.14; distributional bound and Y-quantity bounds: 5.17, 5.20a–b). See the paper’s equations and surrounding text for context and statements: generalized Fano and expectation bound (5.12–5.14) , the modeling setup and definitions (5.1–5.11) , the Pinsker-type inequality (5.17) , and the Y-quantity bounds (5.20a–b) with modeling implications .