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

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Nonlinear Dynamics

Background:

• Stochastic thermodynamics analyzes systems operating far from equilibrium.
• Heat engines convert thermal energy into work.
• Two-particle Langevin systems offer a tractable model for complex thermodynamic phenomena.

Purpose of the Study:

• Investigate the stochastic thermodynamics of a two-particle Langevin system.
• Analyze its performance as an autonomous heat engine.
• Determine the efficiency at maximum power and its universality.

Main Methods:

• Analytical examination of thermodynamic properties due to system linearity.
• Derivation of the efficiency at maximum power (ηMP).
• Obtaining the large deviation function for stochastic efficiency in the overdamped limit.

Main Results:

• The engine's efficiency at maximum power is ηMP = 1 - sqrt[T2/T1].
• This universal form, previously seen in endoreversible engines, is extended to non-endoreversible systems.
• The large deviation function for stochastic efficiency exhibits specific behavior related to macroscopic efficiency.

Conclusions:

• The study extends the universal efficiency behavior of heat engines to non-endoreversible systems.
• Analytical tractability of the linear system allows for precise thermodynamic property examination.
• The findings contribute to understanding energy conversion in small, driven systems.