Operational characteristics of single-particle heat engines and refrigerators with time-asymmetric protocol

We have studied the single-particle heat engine and refrigerator driven by time asymmetric protocol of finite duration. Our system consists of a particle in a harmonic trap with time-periodic strength that drives the particle cyclically between two baths. Each cycle consists of two isothermal steps at different temperatures and two adiabatic steps connecting them. The system works in irreversible mode of operation even in the quasistatic regime. This is indicated by finite entropy production even in the large cycle time limit. Consequently, Carnot efficiency for heat engine or Carnot coefficient of performance (COP) for refrigerators is not achievable. We further analyzed the phase diagram of heat engines and refrigerators. They are sensitive to time-asymmetry of the protocol. Phase diagram shows several interesting features, often counterintuitive. The distribution of stochastic efficiency and COP is broad and exhibits power-law tails.