Electrochemistry bridges chemistry, materials science, biomolecular science, and mathematics to explain how electrical and chemical processes interact at the atomic scale. It underpins critical technologies—including batteries, fuel cells, electrolyzers, metal separation, and green-chemical synthesis—and provides a scientific foundation for sustainable technologies addressing renewable-energy integration, carbon reduction, and resource efficiency. Electrochemical interfaces also play a central role in biology, enabling molecular probing, diagnostics, and nanoscale bioelectronic technologies.

Despite this broad impact, electrochemical reactions occur in an environment that is exceptionally difficult to interrogate directly: the solid–liquid interface. Experiments typically access only macroscopic observables—applied voltages, ionic concentrations, electrolyte composition—while the microscopic structure and dynamics must be inferred indirectly. Deterministic continuum models, which describe averaged electrostatic potentials and ion distributions normal to an interface, historically provided the essential link between atomic-scale processes and signals measured by potentiostats, galvanostats, cyclic voltammetry, and impedance spectroscopy.

However, recent experimental and ab initio simulation advances reveal that electrochemical interfaces exhibit large statistical fluctuations in the electrostatic potential—in the order of one volt. These fluctuations profoundly influence molecular ordering, interfacial structure, adsorption, and reaction kinetics. They also challenge the assumptions underlying deterministic continuum descriptions, which smooth out precisely the spatial and temporal variations that govern interfacial chemistry. While ab initio simulations capture these fluctuations and provide mechanistic insight, they remain far too computationally intensive for the large spatial domains and high-throughput explorations needed to guide materials discovery and connect to experiment.

To move beyond these limitations, stochastically informed interaction-kernel models provide a scalable mathematical framework that retains the efficiency of continuum approaches while incorporating fluctuation statistics learned from atomistic simulations. By training interaction kernels on stochastically driven data, these models explicitly account for oscillatory water structure, fluctuating dielectric response, and rare but chemically decisive field fluctuations that deterministic models systematically miss. This stochastic, kernel-based modeling paradigm—successful in physics, biology, finance, and engineering—remains largely unexplored in electrochemistry but holds significant promise for unifying atomic-scale insight with macroscale predictability.

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