Marbles and Bottles-or Boxes illustrate Irreversibility and Recurrence

Abstract

Imaginary assemblies of intercommunicating bottles-or boxes, in which marbles circulate performing random walks, can help modeling (and hence understanding) slow and long-lasting diffusion processes and enable easy evaluations of typical times involved in their dynamics. Compared to the more traditional approaches to explaining diffusion inspired by the Ehrenfest's urn problem, these simple random walk models offer a more straightforward way to illustrate irreversibility/recurrence issues.