= Smoluchowski equation
{c}
{title2=$\partial_t p=D\nabla\cdot(\nabla p+\beta p\nabla U)$}
For overdamped <Brownian motion> at uniform <temperature> in a <potential energy> $U$, constant <diffusion coefficient> $D$ gives the displayed <Fokker-Planck equation>, with $\beta=(k_BT)^{-1}$. The <probability current> is $\boldsymbol J=-D(\nabla p+\beta p\nabla U)$. Zero current recovers the <Boltzmann distribution>; absorbing boundaries instead permit transport and <mean first-passage times>. This diffusion equation should be distinguished from the similarly named coagulation equation.
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