How Many Kelvins Are Equivalent to One Electron-Volt: An Investigation of Energy-Temperature Scaling in Catalysis.

Classical thermodynamics equates 1 eV to ∼11,606 K, yet reactions associated with eV-scale barriers can still proceed at ∼300 K. In open, driven catalytic systemsparticularly photocatalysisthe rate-relevant energy populations may deviate substantially from equilibrium Maxwell-Boltzmann statistics, and the bath temperature alone is therefore not a sufficient descriptor of reactivity, which can be traced in the work of Montroll and Shuler in 1957 (MontrollE. W., ; ShulerK. E., Studies in Nonequilibrium Rate Processes. I. The Relaxation of a System of Harmonic Oscillators. The Journal of Chemical Physics1957, 26 (3), 454-464. DOI: 10.1063/1.1743326). Here we extend a quantum-mechanical kinetic framework to quantify how photoexcitation and relaxation shape a nonequilibrium distribution over discrete molecular/surface states. We show that the effective energetic availability for barrier crossing, Ψ, becomes context dependent. This dependence is governed by intermolecular or adsorbate-surface interaction strengths and relaxation pathways. The resulting picture rationalizes why apparent eV-scale activation parameters can coexist with ambient bath temperatures. Our work thus introduces a model of context-dependent energy transduction, offering a new principle for understanding catalytic processes by bridging quantum energy scales with macroscopic kinetics.