rateEnhancement
plain-language theorem explainer
Rate enhancement is defined as the ratio of Boltzmann factors for the catalyzed and uncatalyzed activation barriers. Enzyme kineticists cite it to quantify how barrier reduction accelerates reactions inside the J-cost landscape model. The definition is a direct algebraic quotient of two exponential terms.
Claim. The rate enhancement factor is $r = e^{-E_ {cat}/kT} / e^{-E_{uncat}/kT}$, where $E_{uncat}$ and $E_{cat}$ are the activation energies of the uncatalyzed and catalyzed paths and $kT$ is the thermal energy.
background
Activation energy barriers emerge from the J-cost landscape in Recognition Science chemistry. The transition state is the maximum J-cost point along the reaction coordinate, and rates follow Boltzmann statistics over this landscape, recovering the Arrhenius form. The Boltzmann factor is the exponential $e^{-E_a/kT}$.
proof idea
This is a one-line definition that divides the Boltzmann factor evaluated at the catalyzed barrier by the factor at the uncatalyzed barrier.
why it matters
The definition is invoked in the theorem establishing that enzyme catalysis yields rate >1 when the barrier drops. It implements the RS claim that enzymes reshape the J-cost profile to lower the transition-state maximum while preserving overall energetics, and it connects directly to the emergence of Arrhenius kinetics from J-cost.
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