Performance analysis for Feynman's ratchet as a refrigerator with heat leak under different figure of merits

The performance of Feynman's ratchet refrigerator with heat leak has been studied under the maximum COP, maximum cooling rate and maximum χ figure of merits. The χ criterion considers both the COP and cooling rate, which can been seen as a trade-off between COP and cooling rate. Therefore the traditional performance region between maximum cooling rate and maximum COP can be divided into two more specific ones (the region between maximum cooling rate and maximum χ, and the region between maximum χ and maximum COP), which represent two different operating demands. The results shows that the operating parameters such as heat leak, external moment, intrinsic energy potential and the Carnot COP have significant impacts on the performance of the Feynman's ratchet refrigerator. If the parameters are properly chosen, the refrigerator can be controlled to operate within the optimal regimes to fulfill the actual specified demands. Furthermore, for given Carnot COP and heat leak, there exist upper bounds for the maximum value of the maximum COP, maximum cooling rate and maximum χ, respectively.