The Clausius-Mossotti formula
Mitia Duerinckx, Antoine Gloria
TL;DR
This paper offers a concise, robust proof of the Clausius-Mossotti formula for effective conductivity in dilute systems, with optimal error estimates, applicable broadly under minimal assumptions.
Contribution
It presents a new, simplified proof of the Clausius-Mossotti formula that requires only stationarity and ergodicity, extending its applicability.
Findings
Provides an optimal error estimate for the formula.
Proves the formula under minimal assumptions.
Applicable to various dilute systems.
Abstract
In this note, we provide a short and robust proof of the Clausius-Mossotti formula for the effective conductivity in the dilute regime, together with an optimal error estimate. The proof makes no assumption on the underlying point process besides stationarity and ergodicity, and can be applied to dilute systems in many other contexts.
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Taxonomy
TopicsAdvanced Thermodynamics and Statistical Mechanics · Theoretical and Computational Physics · Markov Chains and Monte Carlo Methods