Numerical Evidence for Thermally Induced Monopoles

Electrical charges are conserved. The same would be expected to hold for magnetic charges, yet magnetic monopoles have never been observed. It is therefore surprising that the laws of non-equilibrium thermodynamics, combined with Maxwell's equations, suggest that colloidal particles heated or cooled in certain polar or paramagnetic solvents may behave as if they carry an electrical/magnetic charge [J. Phys. Chem. B $\textbf{120}$, 5987 (2016)]. Here we present numerical simulations that show that the field distribution around a pair of such heated/cooled colloidal particles agrees quantitatively with the theoretical predictions for a pair of oppositely charged electrical or magnetic monopoles. However, in other respects, the non-equilibrium colloids do not behave as monopoles: they cannot be moved by a homogeneous applied field. The numerical evidence for the monopole-like fields around heated/cooled colloids is crucial because the experimental and numerical determination of forces between such colloids would be complicated by the presence of other effects, such as thermophoresis.