PreprintCC BY 4.0arXiv
Einstein's theory of Brownian motion: The non-Fickian normal diffusion
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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BibTeX
@misc{bhattacharyay2026einsteins,
title = {{Einstein's theory of Brownian motion: The non-Fickian normal diffusion}},
author = {A. Bhattacharyay},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30194},
eprint = {2610.30194},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30194},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Einstein's theory of Brownian motion: The non-Fickian normal diffusion
AU - A. Bhattacharyay
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30194
UR - https://arxiv.org/abs/2610.30194
AB - 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.
ER -