A 2D Infrared Catastrophe and the Quantum Limits of Voltage Noise in Water

Electrostatic potential fluctuations in liquid water control the thermodynamics and kinetics, such the solvation free energies, the capacitance of electrified interfaces, and the decoherence of molecular qubits in aqueous environments. Most simulation work has focused on mean fields. Only recently has it become clear that the fluctuations themselves carry physics that is missed by the average. Yet it is far from obvious how much of what slab simulations report as voltage noise is signal and how much is artifact. In this talk I will argue that a sizable part of what is currently reported is a boundary-condition pathology — a 2D analogue of the infrared catastrophes familiar from QED and the ultraviolet problem — and that once it is removed, the genuine voltage noise of water has a clean quantum origin that can be read off the experimentally measured dielectric function.
This talk will first show how lateral 2D periodicity injects an unscreened mode, causing the variance of the plane-averaged potential to diverge linearly with distance from the electrode. It will then turn to the genuine fluctuation spectrum, derived from the quantum fluctuation–dissipation theorem and the measured dielectric function of water: the true thermal RMS fluctuation is about 0.2 V on nanometer scales, while classical simulations overestimate it by an additional ~70% beyond the divergence itself. Finally, the talk will discuss what these bounds imply for solvation, electron transfer, and the choice of water model and slab geometry in situations where fluctuations, rather than mean fields alone, govern the chemistry.