Irreducible Memory in Open Chemical Systems: Non Markovianity, Non Compressibility, and Selection Inequivalence

This work studies nonlinear reaction-diffusion systems coupled to partially observable environments with long-range temporal correlations. Using the Nakajima-Zwanzig projection formalism, the paper derives conditions under which the resulting memory kernel develops non-removable branch-cut structure in Laplace space, preventing finite-dimensional Markovian embedding. The framework further establishes non-compressibility of environmental history and history-dependent attractor selection under memory-driven environmental coupling. Renormalization-group analysis and numerical validation are provided for systems driven by 1/f environmental noise.