Optimal driving protocols for nano-sized devices and their dependence on couplings to reservoirs

Abstract

The development of efficient artificial nanodevices poses challenges which are of fundamental and technological nature. Recent progress has been made in the context of finite-time thermodynamics. A central question in finite-time thermodynamics is to identify the optimal procedure to extract the greatest amount of work from a system operating under well-defined constraints. For externally controlled small systems, the optimal driving protocol maximizes the mean work spend in a finite-time transition between two given system states under the constraints of given initial and final energy values, and a fixed total operation time. For simplicity we consider an externally controlled single level system, which is embedded in a thermal environment and coupled to a particle reservoir. The optimal protocols are calculated from a master equation approach for different system-reservoir couplings. For open systems, the system-reservoir couplings are shown to have a striking influence on the optimal driving setup. We point out that the optimal protocols have discontinuous jumps at the initial and final times. Finally, this work provides a first attempt to extend these calculations to larger system sizes.