Entropic anomaly and maximal efficiency of microscopic heat engines

摘要

The efficiency of microscopic heat engines in a thermally heterogenous environment is considered. We shownthat—as a consequence of the recently discovered entropic anomaly—quasistatic engines, whose efficiency isnmaximal in a fluid at uniform temperature, have in fact vanishing efficiency in the presence of temperaturengradients. For slow cycles the efficiency falls off as the inverse of the period. The maximum efficiency is reachednat a finite value of the cycle period that is inversely proportional to the square root of the gradient intensity. Thenrelative loss in maximal efficiency with respect to the thermally homogeneous case grows as the square root ofnthe gradient. As an illustration of these general results, we construct an explicit, analytically solvable example ofna Carnot stochastic engine. In this thought experiment, a Brownian particle is confined by a harmonic trap andnimmersed in a fluid with a linear temperature profile. This example may serve as a template for the design of realnexperiments in which the effect of the entropic anomaly can be measured.