Faraday law, oxidation numbers, and ionic conductivity: The role of topology

TL;DR

This paper explores the topological basis of Faraday's law, oxidation states, and ionic conductivity, providing a many-body theoretical framework that unifies these phenomena and clarifies their underlying topological nature.

Contribution

It introduces a many-body generalization of the topological interpretation of Faraday's law, oxidation numbers, and ionic conductivity, offering new insights and simplified formulas.

Findings

Faraday's experiment measures topologically quantized charge transport.

Oxidation states in insulating liquids are topologically unambiguous.

Topology significantly influences ionic conductivity in insulating liquids.

Abstract

Faraday's experiment measures -- within a modern view -- the charge adiabatically transported over a macroscopic distance by a given nuclear species in insulating liquids: the reason why it is integer is deeply rooted in topology. Whole numbers enter chemistry in a different form: atomic oxidation states. They are not directly measurable, and are determined instead from an agreed set of rules. Insulating liquids are a remarkable exception: Faraday's experiment indeed measures the oxidation numbers of each dissociated component in the liquid phase, whose topological values are unambiguous. Ionic conductivity in insulating liquids is expressed in terms of the autocorrelation function of the fluctuating charge current at a given temperature in zero electric field; topology plays a major role in this important observable as well. The existing literature deals with the above issues by adopting the independent-electron framework; here I provide the many-body generalization of all the above findings, which furthermore allows for compact and very transparent notations and formulas.