The 1/e Efficiency Bound: A Mathematical Universality Class with Verified Physical Realizations

We establish that the mathematical constant 1/e ≈ 0.368 represents a fundamental efficiency bound for systems optimizing under extensive irreversibility, constituting an emergent universality class across quantum and classical domains. We prove a conditional inevitability theorem: in any system where accessibility loss is multiplicative, independent, and extensive, the optimal operating point necessarily yields efficiency η* = 1/e. This places the 1/e bound at the same epistemic level as Carnot efficiency, Shannon capacity, and Landauer's limit—not as an absolute law, but as an inevitable consequence of minimal physical axioms.Through numerical simulations with explicit axiom verification, we confirm that seven independent quantum systems belong to this universality class: biological quantum systems (FMO, Cryptochrome-4, Photolyase, LHCII), engineered quantum systems (feedback-controlled MIPT), and quantum communication protocols (Werner distillation, quantum repeaters). The weighted mean yields K̃_c = 0.363 ± 0.005 (1.4% deviation from 1/e); for natural systems only, K̃_c = 0.345 ± 0.015 (6% deviation). Statistical analysis yields p < 10⁻⁷ against random clustering, with Bayesian evidence BF > 1000. Preliminary simulations in ecology (optimal foraging) and economics (optimal stopping) demonstrate identical 1/e convergence when axioms are satisfied, suggesting true cross-domain universality. Seven counterexamples with quantified axiom violations delimit the domain of validity.