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 (Montroll, E. W.; Shuler, K. E. Studies in Nonequilibrium Rate Processes.
I. The Relaxation of a System of Harmonic Oscillators. The Journal of Chemical Physics 1957, 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.