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arXiv · 2610.30194

Einstein's theory of Brownian motion: The non-Fickian normal diffusion

A. Bhattacharyay
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Abstract

Einstein's theory of diffusion defines what is considered {\it normal diffusion}. Historically, Einstein considered homogeneous diffusion characterised by a diffusion constant in his original calculations, resulting in what is known as {\it Fickian} diffusion, which thermally relaxes concentration inhomogeneities. However, in the same derivation of Einstein, the seed of generalisation of the theory to {\it non-Fickian} diffusion in the presence of space-dependent diffusivity is hidden. This indicates that non-Fickian diffusion, which can drive concentration inhomogeneities, can also be normal diffusion. The present article discusses the origin of the {\it normal} non-Fickian diffusion in Einstein's theory of diffusion.

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A. Bhattacharyay. 2026-10-21. Einstein's theory of Brownian motion: The non-Fickian normal diffusion. https://arxiv.org/abs/2610.30194

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