Universal scaling of electrochemical information transfer at solid-liquid interfaces
Electrochemical potentials at solid-liquid interfaces govern diverse chemical and energy conversion processes; however, the extent to which their electrochemical influence extends into the solid remains unclear. Here, we show that the maximum accessible electrochemical information is governed by a single dimensionless screening parameter $u$, defined as the ratio of the effective electrostatic separation between the interface and probe to the electrostatic propagation length in the solid. The maximum Fisher information follows a universal inverse-square scaling with this parameter. This relation identifies electrostatic screening as a fundamental constraint on information transfer across solid-liquid interfaces and provides quantitative design principles for interfacial electrochemical sensing.