Curzon-Ahlborn-type efficiency in a Brownian heat engine with exponential temperature profile

Area of Science:

• Mesoscopic thermodynamics
• Statistical mechanics
• Non-equilibrium systems

Background:

• Brownian motors and heat engines are crucial for understanding energy conversion at the nanoscale.
• Experimental control over thermal gradients, like laser-induced or thermoplasmonic effects, enables realization of specific temperature profiles.
• Endoreversible thermodynamics provides a framework for analyzing heat engines with internal irreversibilities.

Purpose of the Study:

• To investigate a Brownian heat engine operating under an exponential temperature profile.
• To derive exact analytical expressions for key thermodynamic quantities.
• To rigorously connect microscopic stochastic dynamics to macroscopic thermodynamic behavior.

Main Methods:

• Analytical derivation of particle current, thermodynamic efficiency, entropy production, and coefficient of performance (COP).
• Analysis of a Brownian particle in a periodic ratchet potential with an exponentially decreasing temperature.
• Numerical simulations for extended systems of interacting Brownian motors.

Main Results:

• Exact analytical solutions obtained for particle current, efficiency, entropy production, and COP.
• Recovery of Curzon-Ahlborn efficiency and endoreversible COP in the quasistatic limit.
• Demonstration of trade-offs: exponential profile yields higher velocity and entropy production but lower efficiency compared to linear profiles.

Conclusions:

• The study provides a rare, rigorous mesoscopic realization of endoreversible thermodynamics from first principles.
• Efficiency and COP are bounded by the Carnot limit, reflecting inherent irreversibility.
• Exponential temperature profiles offer a tractable and experimentally viable platform for studying nonequilibrium dynamics.