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.

We present a new approach to determining the equilibrium structure of a closed (canonical) inhomogeneous fluid which combines grand canonical density functional theory and a series expansion of the distribution functions in powers of $\left(1/\overline{N}\right)$, where $\overline{N}$ is the average number of particles. For hard spheres in a hard spherical cavity, comparison with canonical Monte Carlo results shows that the method is rather accurate, even for small values of $\overline{N}$. In certain (high packing) situations the density profile develops a pronounced peak in the center of the cavity. Accounting properly for such peaks provides a severe test of any density functional approximation.

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.

The efficiency of four different and representative models of heat engines under maximum conditions for a figure of merit representing a compromise between useful energy and lost energy (the $\Omega${} criterion) is investigated and compared with previous results for the same models where the efficiency is considered at maximum power conditions. It is shown that the maximum $\Omega${} regime is more efficient and, additionally, that the resulting efficiencies present a similar behavior. For each performance regime we obtain explicit equations accounting for lower and upper bounds. The optimization of refrigeration devices is far from being as clear as heat engines, and some remarks on it are finally considered.

The optimum performance of a regenerative Brayton cycle was analyzed. The model includes external and internal irreversibilities coming from four main sources: coupling to external heat reservoirs, turbine and compressor nonisentropic processes, pressure losses in the heater and the cooler, and the regenerator. In terms of the parameters accounting for each type of irreversibility, explicit numerical results are presented for the maximum efficiency, maximum power output, efficiency at maximum power output, power output at maximum efficiency, as well as for the pressure ratios required for maximum efficiency and maximum power. This analysis could provide a general theoretical tool for the optimal design and operation of real regenerative gas turbine power plants.