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.

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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 Ω 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 Ω 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.

We present a density-functional approach for dealing with inhomogeneous fluids in the canonical ensemble. A general relation is proposed between the free-energy functionals in the canonical and the grand canonical ensembles. The minimization of the canonical-ensemble free-energy functional gives rise to Euler-Lagrange equations which involve averaged Ornstein-Zernike equations of second and third order. The theory is especially appropriate for systems with a small, fixed number of particles. As an example of application we obtain accurate results for the density profile of a hard-sphere fluid in a closed spherical cavity that contains only a few particles.

When thermodynamic properties of a pure substance are transformed to reduced form by using both critical- and triple-point values, the corresponding experimental data along the whole liquid-vapor coexistence curve can be correlated with a very simple analytical expression that interpolates between the behavior near the triple and the critical points. The leading terms of this expression contain only two parameters: the critical exponent and the slope at the triple point. For a given thermodynamic property, the critical exponent has a universal character but the slope at the triple point can vary significantly from one substance to another. However, for certain thermodynamic properties including the difference of coexisting densities, the enthalpy of vaporization, and the surface tension of the saturated liquid, one finds that the slope at the triple point also has a nearly universal value for a wide class of fluids. These thermodynamic properties thus show a corresponding apparently universal behavior along the whole coexistence curve.