Universality of maximum-work efficiency of a cyclic heat engine based on a finite system of ultracold atoms.

We study the performance of a cyclic heat engine which uses a small system with a finite number of ultracold atoms as its working substance and works between two heat reservoirs at constant temperatures T _h and T _c (<T _h ). Starting from the expression of heat capacity which includes finite-size effects, the work output is optimized with respect to the temperature of the working substance at a special instant along the cycle. The maximum-work efficiency η ^mw at small relative temperature difference can be expanded in terms of the Carnot value [Formula: see text], [Formula: see text], where a ₀ is a function depending on the particle number N and becomes vanishing in the symmetric case. Moreover, we prove using the relationship between the temperatures of the working substance and heat reservoirs that the maximum-work efficiency, when accurate to the first order of η _C , reads [Formula: see text](ΔT ² ). Within the framework of linear irreversible thermodynamics, the maximum-power efficiency is obtained as [Formula: see text](ΔT ² ) through appropriate identification of thermodynamic fluxes and forces, thereby showing that this kind of cyclic heat engines satisfy the tight-coupling condition.