Abstract
<title>Abstract</title> <p>How do complex systems, from ecosystems to cities, balance internal organization with external exchanges? We introduce a Shannon entropy-partitioning framework for open flow networks and apply it to 74 empirical systems, including natural ecosystems, urban metabolisms and industrial networks. The framework separates internal flow disorder, boundary exchange diversity and dissipative losses, using normalized entropies as information-theoretic descriptors rather than direct measurements of thermodynamic entropy production. It provides an operational way to examine the tension between maximum-power arguments and entropy-production minimization by identifying configurations where robustness and adaptability are jointly high. We find that 84.4% of natural ecosystems, but only 38.1% of urban systems, occupy this organization–adaptability window. Constrained null models preserving boundary conditions, active topology and total internal throughput confirm that this signal is not explained by topology or boundary forcing alone, with median z-scores of 36.1 and 8.7 for organization and adaptability. Pareto front analysis indicates that urban systems such as Suzhou are displaced from the window mainly by insufficient boundary exchange diversity relative to internal flow disorder. Entropy partitioning therefore provides a comparative diagnostic for assessing the thermodynamic organization of ecological, urban and industrial flow systems.</p>