Scientific Reports

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

Zhuolin Ye, Yingying Hu, Jizhou He, Jianhui Wang

Published Jul 18, 2017• 9 citations

Abstract

Abstract 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 (

DOI: 10.1038/s41598-017-06615-z

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Scientific Reports

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

Zhuolin Ye, Yingying Hu, Jizhou He, Jianhui Wang

Published Jul 18, 2017• 9 citations

Publisher

Abstract

DOI: 10.1038/s41598-017-06615-z

Related papers

Efficiency at maximum power of a heat engine working with a two-level atomic system

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{T}_{h}

and

{T}_{c}

(<

{T}_{h})

, is a quantum version of the classical Otto cycle. By optimizing the power output with respect to two frequencies, we obtain the efficiency at maximum power output (EMP) and analyze numerically the effects of the times taken for two adiabatic and two isochoric processes on the EMP. In the absence of internally dissipative friction, we find that the EMP is bounded from the upper side by a function of the Carnot efficiency ${\ensuremath{\eta}}_{C}$, ${\ensuremath{\eta}}_{+}={\ensuremath{\eta}}_{C}^{2}/[{\ensuremath{\eta}}_{C}\ensuremath{-}(1\ensuremath{-}{\ensuremath{\eta}}_{C})\mathrm{ln}(1\ensuremath{-}{\ensuremath{\eta}}_{C})]$, with ${\ensuremath{\eta}}_{C}=1\ensuremath{-}{T}_{c}/{T}_{h}$. This analytic expression is confirmed by our exact numerical result and is identical to the one derived in an engine model based on a mesoscopic or macroscopic system. If the internal friction is included, we find that the EMP decreases as the friction coefficient increases.

We consider the efficiency at maximum power of a quantum Otto engine, which uses a spin or a harmonic system as its working substance and works between two heat reservoirs at constant temperatures

{T}_{h}

and

{T}_{c}

(<{T}_{h})

. Although the behavior of spin-

1/2

system differs substantially from that of the harmonic system in that they obey two typical quantum statistics, the efficiencies at maximum power based on these two different kinds of quantum systems are bounded from the upper side by the same expression ${\ensuremath{\eta}}_{\mathrm{mp}}\ensuremath{\le}{\ensuremath{\eta}}_{+}\ensuremath{\equiv}{\ensuremath{\eta}}_{C}^{2}/[{\ensuremath{\eta}}_{C}\ensuremath{-}(1\ensuremath{-}{\ensuremath{\eta}}_{C})ln(1\ensuremath{-}{\ensuremath{\eta}}_{C})]$ with ${\ensuremath{\eta}}_{C}=1\ensuremath{-}{T}_{c}/{T}_{h}$ as the Carnot efficiency. This expression ${\ensuremath{\eta}}_{\mathrm{mp}}$ possesses the same universality of the CA efficiency ${\ensuremath{\eta}}_{\mathrm{CA}}=1\ensuremath{-}\sqrt{1\ensuremath{-}{\ensuremath{\eta}}_{C}}$ at small relative temperature difference. Within the context of irreversible thermodynamics, we calculate the Onsager coefficients and show that the value of ${\ensuremath{\eta}}_{\mathrm{CA}}$ is indeed the upper bound of EMP for an Otto engine working in the linear-response regime.