Coefficient of performance at maximum χ-criterion of thermochemical refrigerators with near-independent particles

Thermochemical refrigerators, constituted by a cold/hot reservoir with an energy filter between them, are established by utilizing Maxwell–Boltzmann, Fermi–Dirac, and Bose–Einstein particles as working substances. With the help of chemical potential gradient, heat coupled with the particle flux can be transferred against the temperature gradient, thus the cold reservoir is cooled. The coupling between the heat and particle fluxes, determined by the width Γ of the energy filter, will be weakened when Γ increases. As the coupling gets weak gradually, the εC-dependent coefficient of performances (COPs) of such refrigerators are optimized under the χ-criterion, where εC is the Carnot COP and χ is defined as the product of the COP and cooling rate. It is found three different regions of COP at maximum χ in three different kinds of near-independent systems respectively. The corresponding three upper bounds, obtained from the case of strong coupling (i.e., Γ→0), are also bounded by 9+8εC−3∕2 from above. When Γ increases from 0 to infinity, the COPs at maximum χ decreases monotonously to three lower bounds. In addition, the upper bound of Bose–Einstein system can be approximated by the Curzon–Ahlborn COP: εCA=1+εC−1.