How Many Kelvins are Equivalent to One Electron Volt: An Investigation of Unit Conversion in Catalysis

Classical thermodynamics equates 1 eV to ~11,606 K, yet reactions with eV-scale barriers proceed readily at 300 K. This paradox, stemming from the misapplication of equilibrium statistics to quantum processes, exposes the limitations of Boltzmann scaling for non-equilibrium reaction dynamics, which can be traced in the work of Montroll and Shuler1 in 1957 . We resolve this by extending a quantum mechanical model to show that the initial non-equilibrium energy distribution in photocatalysis redefines the eV-K relationship. In our framework, this unit conversion is not a fixed constant but is determined by the balance between potential (eV) and kinetic (K) energy, controlled by intermolecular interaction strength. This decouples reactivity from thermal temperature, allowing for pathway-specific control. Our work thus replaces the classical paradigm with a model of context-dependent energy transduction, offering a new principle for catalyst design by bridging quantum energy scales with macroscopic kinetics.