Intrinsic irreversibility limits the efficiency of multidimensional molecular motors

We consider the efficiency limits of Brownian motors able to extract work from the temperature difference between reservoirs or from external thermodynamic forces. These systems can operate in a variety of modes, including as isothermal engines, heat engines, refrigerators, and heat pumps. We derive analytical results showing that certain classes of multidimensional Brownian motor, including the Smoluchowski-Feynman ratchet, are unable to attain perfect efficiency (Carnot efficiency for heat engines). This demonstrates the presence of intrinsic irreversibilities in their operating mechanism. We present numerical simulations showing that in some cases the loss process that limits efficiency is associated with vortices in the probability current.