Stochastic energetics of a Brownian motor and refrigerator driven by non-uniform temperature

Details Stochastic energetics of a Brownian motor and refrigerator driven by non-uniform temperature Stochastic energetics of a Brownian motor and refrigerator driven by non-uniform temperature

2009-07-05

arxiv.org/abs/0907.0829v1

Physics

Condensed Matter

Statistical Mechanics

15 pages, 9 figures

Scientific paper

The energetics of a Brownian motor and refrigerator driven by position dependent temperature, known as the B{\"u}ttiker-Landauer motor and refrigerator, is investigated by extensive numerical simulations of the inertial Langevin equation. Our results are qualitatively different compared to previous works based on the overdamped Langevin equation and other phenomenological approaches. We find that the irreversible heat transfer via kinetic energy greatly reduces the efficiency/coefficient of performance of the motor/refrigerator. The motor and refrigerator work with maximum efficiency and coefficient of performance at optimal values of mass and friction coefficient but can never reach the Carnot efficiency/coefficient of performance. We also study the behavior of the motor in the linear response regime under condition of maximum power and find that efficiency at maximum power can never reach the efficiency of an endoreversible engine working at maximum power: the Curzon-Ahlborn efficiency. Under an analogous condition equivalent to that of maximum power, the coefficient of performance of the refrigerator cannot reach the coefficient of performance reached by a Carnot engine. Predictions of linear irreversible thermodynamics are in good agreement with numerical data. Finally, we investigate the role of different potential and temperature profiles to reduce the irreversible kinetic energy contribution. and increase the motor efficiency and refrigerator coefficient of performance. Our simulations show that optimizing the potential and temperature profile in order to reduce the irreversible heat transfer, diminishes the particle current as well leading only to a marginal enhancement of the system performance.

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