Exploring outputs from concatenated stochastic heat engines

Recent work on the concatenation of two simple heat engines has shown that it may lead to non-monotonic variations in the efficiency and power with parameters like driving amplitudes and asymmetries in cycle periods. Motivated by this study, we investigate the effect of the concatenation between two stochastic heat engines where colloidal particles have been trapped in harmonic potentials. The stiffness parameters of each engine are varied cyclically, but with different cycle periods, with a common thermal bath that acts as a sink for the first engine but as a source for the second. We consider two types of protocol, the first where the trap strength undergoes sudden jumps, and the second where it varies linearly with time. In both we find several non-trivial effects, like the non-monotonic functional dependence of the engine outputs on several parameters used in the setup. For the protocol that varies linearly with time, the concatenation leads to enhanced output power as compared to a single effective engine, in a suitable range of parameters. It has been shown that the output from the combined system shows a peak with respect to the asymmetry in the cycle times of the engines that have been concatenated. A general relation for the efficiency of an arbitrary number of concatenated engines driven quasistatically has been provided.