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 an 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 a 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.

中文翻译：

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法拉第定律、氧化数和离子电导率：拓扑的作用

法拉第的实验在现代观点中测量了绝缘液体中给定核物质在宏观距离上绝热传输的电荷：它是整数的原因深深植根于拓扑学。整数以不同的形式进入化学：原子氧化态。它们不能直接测量，而是由一组商定的规则确定。绝缘液体是一个显着的例外。Faraday 的实验确实测量了液相中每个解离组分的氧化数，其拓扑值是明确的。绝缘液体中的离子电导率用零电场中给定温度下波动充电电流的自相关函数表示；拓扑在这个重要的可观察对象中也起着重要作用。现有文献采用独立电子框架处理上述问题；在这里，我提供了所有上述发现的多体概括，此外，这允许紧凑且非常透明的符号和公式。