Einstein2: Brownian motion meets general relativity

Abstract

Blending general relativity with Brownian motion theory leads to an interesting prediction: the classical root-of-time behavior of the RMS displacement of a Brownian particle is affected by gravity. These corrections to the diffusion law are not just a theoretical curiosity: they provide an opportunity for a new kind of "metamaterials", where diffusive transport - as opposed to ray propagation, as in transformation optics - can be tailored with suitably designed effective metrics. What is more, this effect force us to reconsider the formulation of the second law of (non-equilibrium) thermodynamics in gravitational analogues, as tracers diffusing in curved effective metrics can sometimes accumulate (instead of spreading), thereby decreasing their Gibbs entropy, without any force being applied to them. © Springer International Publishing Switzerland 2013.