Performance characteristics and parametric optimum criteria of a Brownian micro-refrigerator in a spatially periodic temperature field

It is shown that a microscopic system consisting of Brownian particles moving in a spatially asymmetric but periodic potential (ratchet) and contacting with the alternating hot and cold reservoirs along space coordinate and an external force applying on the particles may work as a refrigerator. In order to clarify the underlying physical pictures of the system, the heat flows via both the potential energy and the kinetic energy of the particles are considered simultaneously. Based on an Arrhenius’ factor describing the forward and backward particle currents, expressions for some important performance parameters of the refrigerator, such as the coefficient of performance, cooling rate and power input, are derived analytically. The maximum coefficient of performance and cooling rate are numerically calculated for some given parameters. The influence of the main parameters such as the external force, barrier height of the potential, asymmetry of the potential and temperature ratio of the heat reservoirs on the performance of the Brownian refrigerator is discussed. The optimum criteria of some characteristic parameters are given. It is found that the Brownian refrigerator may be controlled to operate in different regions through the choice of several parameters. PACS numbers: 05.40.Jc, 05.70.−a, 05.60.−k (Some figures in this article are in colour only in the electronic version) 1751-8113/09/075006+14$30.00 © 2009 IOP Publishing Ltd Printed in the UK 1 J. Phys. A: Math. Theor. 42 (2009) 075006 B Lin and J Chen