Tu, ZC (reprint author), Beijing Normal Univ, Dept Phys, Beijing 100875, Peoples R China.
; Yang Pan
; Tu Zhan-Chun] Beijing Normal Univ, Dept Phys, Beijing 100875, Peoples R China
; [Tu Zhan-Chun] Chinese Acad Sci, Kavli Inst Theoret Phys China, Beijing 100190, Peoples R China
The x-criterion is defined as the product of the energy conversion efficiency and the heat absorbed per unit time by the working substance [de Tomas et al., Phys. Rev. E 85 (2012) 010104(R)]. The x-criterion for Feynman ratchet as a refrigerator operating between two heat baths is optimized. Asymptotic solutions of the coefficient of performance at maximum x-criterion for Feynman ratchet are investigated at both large and small temperature difference. An interpolation formula, which fits the numerical solution very well, is proposed. Besides, the sufficient condition for the universality of the coefficient of performance at maximum x is investigated.