Efficiency at maximum power output for a passive engine

Abstract

Efficiency at maximum power (MP) output for a passive engine without mechanical controls between two reservoirs is theoretically studied. We enclose a hard core gas partitioned by a massive piston in a temperature-controlled container and analyze the efficiency at MP under a heating and cooling protocol without controlling the pressure acting on the piston from outside. We find the following three results: (i) The efficiency at MP for a dilute gas is close to the Chambadal-Novikov-Curzon-Ahlborn (CNCA) efficiency, while (ii) the efficiency for a moderately dense gas becomes smaller than the CNCA efficiency even when the temperature difference of reservoirs is small. (iii) Introducing the Onsager matrix for passive engines, we verify that the tight coupling condition for the matrix of the dilute gas is satisfied, while that of the moderately dense gas is not satisfied because of the inevitable heat leak. We clarify these results using the molecular dynamics simulation and introducing an effective mean-field-like model which we call stochastic mean field model.