Efficiency at maximum power and efficiency fluctuations in a linear Brownian heat-engine model

We investigate the stochastic thermodynamics of a two-particle Langevin system. Each particle is in contact with a heat bath at different temperatures T1 and T2 (<T1), respectively. Particles are trapped by a harmonic potential and driven by a linear external force. The system can act as an autonomous heat engine performing work against the external driving force. Linearity of the system enables us to examine thermodynamic properties of the engine analytically. We find that the efficiency of the engine at maximum power ηMP is given by ηMP=1-T2/T1. This universal form has been known as a characteristic of endoreversible heat engines. Our result extends the universal behavior of ηMP to nonendoreversible engines. We also obtain the large deviation function of the probability distribution for the stochastic efficiency in the overdamped limit. The large deviation function takes the minimum value at macroscopic efficiency η=η and increases monotonically until it reaches plateaus when η≤ηL and η≥ηR with model-dependent parameters ηR and ηL.