The Rectication Limit: Deriving the 10% Trophic Eciency Rule from Information Thermodynamics

For over 80 years, Lindeman's "10% Rule" of trophic transfer efficiency has served as a cornerstone of ecology, yet it remains an empirical observation without a derivation from first principles. Here, we propose that trophic efficiency is governed by a fundamental limit on irreversible information conversion, η = 2/π ≈ 63.66%, which represents the maximum efficiency of converting a fluctuating energy–matter flux into a stable structural state through an irreversible, entropy-producing process. We demonstrate that the canonical trophic transfer in ectothermic food webs involves a cascade of five distinct irreversible sub-processes — capture, digestion, absorption, anabolism, and retention — predicting a cumulative efficiency of η⁵ ≈ 10.4%. This theoretical value is statistically indistinguishable from the global meta-analytic mean of 10.13% reported for 48 aquatic ecosystem models. Furthermore, we show that the reduced efficiency observed in endotherms (1–5%) corresponds to additional irreversible information costs associated with homeostatic control loops (η⁷ to η⁹). Finally, we introduce the concept of Information Impedance to resolve the apparent anomaly of high assimilation efficiency in carnivores, distinguishing between low-cost structural copying (protein-to-protein transfer) and high-cost structural conversion (cellulose-to-protein transformation). These findings suggest that ecological energy flow is bounded not merely by metabolic constraints, but by the geometry of irreversible information processing.