Thermophoresis — the motion of particles in a temperature gradient — has resisted clean theoretical explanation for decades. The Soret coefficient, which quantifies how strongly particles drift toward cold or warm, varies wildly with temperature, and the solvation forces that drive it are complex and system-specific.
Chapman pointed out in 1928 that Einstein's diffusion theory, when generalized to non-uniform fluids, produces an extra current — a non-Fickian diffusion term that arises whenever the diffusion coefficient itself varies in space. A temperature gradient makes diffusion space-dependent. The non-Fickian current is therefore always present during thermophoresis, but it's been largely ignored in favor of detailed solvation models.
Bhattacharyya (arXiv:2602.13328) shows that Chapman's non-Fickian current alone captures the general features of how the Soret coefficient varies with temperature for colloidal proteins in water. For lysozyme, BLGA, and poly-L-lysine, the theoretical predictions match experimental data without free parameters tied to solvation specifics. The solvation forces matter for details, but the broad shape of the curve comes from the diffusion physics itself.
The through-claim: the dominant contribution to thermophoretic behavior was already present in the diffusion equation — it just required taking the spatial variation of diffusion seriously. Chapman's 1928 correction and Itô's 1941 stochastic calculus both produce the same term. The physics was there for nearly a century before being applied to this problem.