A unified optimization criterion for Carnot engines and refrigerators is proposed. It consists of maximizing the product of the heat absorbed by the working system times the efficiency per unit time of the device, either the engine or the refrigerator. This criterion can be applied to both low symmetric dissipation Carnot engines and refrigerators. For engines the criterion coincides with the maximum power criterion and then the Curzon-Ahlborn efficiency $\eta${}CA=1$-${}Tc/Th is recovered, where Th and Tc are the temperatures of the hot and cold reservoirs, respectively [Esposito, Kawai, Lindenberg, and Van den Broeck, Phys. Rev. Lett. 105, 150603 (2010)]. For refrigerators the criterion provides the counterpart of Curzon-Ahlborn efficiency for refrigerators $\varepsilon${}CA=[1/(1$-${}(Tc/Th)]$-${}1, first derived by Yan and Chen for the particular case of an endoreversible Carnot-type refrigerator with linear (Newtonian) finite heat transfer laws [Yan and Chen, J. Phys. D: Appl. Phys. 23, 136 (1990)].

We propose a unified optimization criterion for energy converters. It represents the best compromise between energy benefits and losses for a specific job and neither an explicit evaluation of entropies nor the consideration of environmental parameters are required. For all considered systems the criterion predicts a performance regime laying between those of maximum efficiency and maximum useful energy. Such regime has been invoked as optimum not only in macroscopic heat engines but also in some molecular motors.

The figure of merit for refrigerators performing finite-time Carnot-like cycles between two reservoirs at temperature $T_h$ and $T_c$ ($<T_h$) is optimized. It is found that the coefficient of performance at maximum figure of merit is bounded between 0 and $(\sqrt{9+8{\varepsilon }_c}-3)/2$ for the low-dissipation refrigerators, where ${\varepsilon }_c=T_c/(T_h-T_c)$ is the Carnot coefficient of performance for reversible refrigerators. These bounds can be reached for extremely asymmetric low-dissipation cases when the ratio between the dissipation constants of the processes in contact with the cold and hot reservoirs approaches to zero or infinity, respectively. The observed coefficients of performance for real refrigerators are located in the region between the lower and upper bounds, which is in good agreement with our theoretical estimation.

An upper bound for the coefficient of performance (COP) of endoreversible refrigerators which depends only on the ratio $\tau {=T}_c/T_h$ between the cold and hot reservoir temperatures has been elusive to date. We address here this long standing problem by analyzing an endoreversible Carnot refrigerator that operates in conditions of maximum per-unit-time COP. Two novel results are obtained: (1) A long sought $\tau$-dependent upper bound for the COP of refrigerators. (2) A $\tau$-dependent optimum distribution of the heat conductances associated with the coupling between the refrigerant and the heat reservoirs. Moreover, when the method is applied to heat engines, the resulting optimum efficiency is even closer to real efficiencies than the well-known Curzon-Ahlborn result.

Arrays of coupled heat engines are proposed as a paradigmatic model to study the trade-off between individual and collective behavior in linear irreversible thermodynamics. The analysis reveals the existence of a control parameter which selects different operation regimes of the whole array. In particular, the regimes of maximum efficiency and maximum power are considered, giving for the latter a general derivation of the Curzon-Ahlborn efficiency which surprisingly does not depend on whether or not the individual engines in the array work at maximum power.

We apply a unified and trade-off based optimization for low-dissipation models of cyclic heat devices which accounts for both useful energy and losses. The resulting performance regime lies between those of maximum first-law efficiency and maximum $\chi$ (a unified figure of merit corresponding to power output of heat engines). The bounds available for both symmetric and extremely asymmetric heat devices are explicitly obtained. The similarities for heat engines and refrigerators and the energetic advantages of the trade-off optimization are especially stressed.