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 η_{M P} is given by η_{M P}=1 -√{T₂/T₁ } . This universal form has been known as a characteristic of endoreversible heat engines. Our result extends the universal behavior of η_{M P} 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 ≤η_L and η ≥η_R with model-dependent parameters η_R and η_L.