boltzmannFactor
plain-language theorem explainer
The Boltzmann factor supplies the dimensionless multiplier exp(-barrier) that converts J-cost saddle heights into relative reaction rates under unit temperature. Kinetic modelers and Recognition Science researchers cite it when deriving catalytic enhancements from complementary enzyme topologies. The definition is implemented as a direct one-line wrapper around the real exponential function.
Claim. For a barrier height $b$, the Boltzmann factor is $e^{-b}$, with thermal energy normalized so that $kT=1$.
background
Recognition Science treats reaction barriers as positive J-cost saddles on a phi-scaled landscape. The EnzymeCatalysis module shows that an ideal enzyme supplies a complementary J-cost profile whose value at the transition-state coordinate exactly cancels the reaction saddle, flattening the total cost to zero. This definition specializes the Boltzmann factor to the dimensionless case used throughout the rate calculations, consistent with the upstream forms in ActivationEnergy and BoltzmannDistribution that retain explicit $kT$.
proof idea
The definition is a one-line wrapper that applies Real.exp to the negated barrier argument.
why it matters
This definition anchors the rate theorems that quantify enzyme action as J-cost cancellation. It is invoked by catalyzedRate, uncatalyzedRate, rate_enhancement, and ideal_enzyme_unit_rate to recover the full activation energy as the ratio of catalyzed to uncatalyzed factors. The construction realizes the Boltzmann step of the module's core claim that enzyme topology is the additive inverse of the transition-state J-cost, thereby linking phi-ladder barriers to observable kinetics.
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