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On the efficiency at maximum cooling power

The efficiency at maximum power (EMP) of heat engines operating as generators is one corner stone of finite-time thermodynamics, the Curzon-Ahlborn efficiency $η_{\rm CA}$ being considered as a universal upper bound. Yet, no valid counterpart to $η_{\rm CA}$ has been derived for the efficiency at maximum cooling power (EMCP) for heat engines operating as refrigerators. In this Letter we analyse the reasons of the failure to obtain such a bound and we demonstrate that, despite the introduction of several optimisation criteria, the maximum cooling power condition should be considered as the genuine equivalent of maximum power condition in the finite-time thermodynamics frame. We then propose and discuss an analytic expression for the EMCP in the specific case of exoreversible refrigerators.