  We point out a surprising feature of diffusion in inhomogeneous media: under
suitable conditions, the rectification of the Brownian paths by a diffusivity
gradient can result in initially spread tracers spontaneously concentrating.
This "geometric ratchet effect" demonstrates that, in violation of the
classical statements of the second law of (non-equilibrium) thermodynamics,
self-organization can take place in thermodynamic systems at local equilibrium
without heat being produced or exchanged with the environment. We stress the
role of Bayesian priors in a suitable reformulation of the second law
accommodating this geometric ratchet effect.
