Coefficient of performance at maximum chi-criterion for Feynman ratchet as a refrigerator

The \chi-criterion is defined as the product of the energy conversion efficiency and the heat absorbed per-unit-time by the working substance [de Tom\'as et al., Phys. Rev. E, 85 (2012) 010104(R)]. The \chi-criterion for Feynman ratchet as a refrigerator operating between two heat baths is optimized. Asymptotic solutions of the coefficient of performance at maximum \chi-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 \chi is investigated.