Minimal model for Brownian vortexes

A Brownian vortex is a noise-driven machine that uses thermal fluctuations to extract a steady-state flow of work from a static force field. Its operation is characterized by loops in a probability current whose topology and direction can change with changes in temperature. We present discrete three- and four-state minimal models for Brownian vortexes that can be solved exactly with a master-equation formalism. These models elucidate conditions required for flux reversal in Brownian vortexes and provide insights into their thermodynamic efficiency through the rate of entropy production.