A Heterogeneity-Corrected Lower Bound on Entropy Production in Nonequilibrium Markov Networks

Version 2 of a preprint studying activity- and heterogeneity-sensitive lower bounds on entropy production in finite nonequilibrium Markov networks. The principal variance coefficient 1/(1 − χ̄²) is identified as a direct specialization of the published Liao–Berg sharpened-Jensen framework and is not claimed as a new general inequality. The thermodynamic development includes an exact heterogeneity decomposition, a certified mixed-moment hierarchy converging to exact entropy production, constructive stationary-ring realizability at fixed activity and mean asymmetry, an explicit finite-ring topology-dependent refinement, and an exact reduction of the globally sharp ring coefficient to finitely many one-dimensional two-activity-level minimizations. Additional results include a one-dimensional diffusion construction in which the bound becomes asymptotically exact and a rigorous finite-sample lower confidence bound under an independent-Poisson directional-count observation model. The manuscript also documents limitations involving coarse-graining and the failure of naive finite-sample plug-in guarantees. The archive contains the manuscript and LaTeX source, verification programs, archived numerical results, figure-generation code, figures, citation metadata, licensing information, and SHA-256 checksums. Novelty and priority have not been independently established.