Self-organization without heat: the geometric ratchet effect

TL;DR

This paper reveals that in inhomogeneous media, diffusion can spontaneously concentrate tracers through a geometric ratchet effect, challenging traditional thermodynamics by enabling self-organization without heat exchange.

Contribution

It introduces the geometric ratchet effect, showing how diffusivity gradients can cause self-organization in thermodynamic systems at equilibrium without heat transfer.

Findings

Diffusivity gradients can rectify Brownian motion leading to concentration.

Self-organization can occur without heat exchange, violating classical second law statements.

Bayesian priors are crucial in reformulating the second law to include this effect.

Abstract

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.