Uphill diffusions in single and multi-species systems

Abstract

Uphill diffusions constitute an intriguing phenomenon reported in a series of numerical simulations and experiments, where particles are observed to move from regions of lower density to regions of higher density, at variance with the basic tenets of transport theory. In this paper we review several examples of uphill currents that appear in quite different frameworks. We highlight the 
role of the coupling with external reservoirs in giving rise to particle currents with the ``wrong'' sign,
and also put forward a statistical mechanical explanation of the phenomenon for multi-species systems as well as for single species models undergoing a phase transition.