Ising model for Brownian donkey

We introduce a thermal engine consisting of N interacting Brownian particle s moving in a periodic potential, featuring an alternation of hot and cold symmetric peaks. A discretized Ising-like version is solved analytically. I n response to an external force, absolute negative mobility is observed for N greater than or equal to 4. For N --> infinity nonequilibrium phase tran sition takes place with a spontaneous symmetry breaking en ailing he appear ance of a current in the absence of an external force.