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.