Brownian micro-engines and refrigerators in a spatially periodic temperature field: Heat flow and performances

We study the thermodynamic features of a thermal motor driven by temperature differences, which consists of a Brownian particle moving in a sawtooth potential with an external load. The motor can work as a heat engine or a refrigerator under different conditions. The heat flow driven by both potential and kinetic energy is considered. The former is reversible when the engine works quasistatically and the latter is always irreversible. The efficiency of the heat engine (Coefficient Of Performance (COP) of a refrigerator) can never approach Carnot efficiency (COP).