Journal of Non-Equilibrium Thermodynamics

Energy production in one-qubit quantum Agrawal machines

Julio J. Fernández

Published Jan 24, 2023• 20 citations

Abstract

Abstract We obtain the power and Ω-function of one-qubit Agrawal quantum heat engines solving the Lindbland equation and using the tools of Finite Time Thermodynamics. We prove that these two thermodynamic functions have their maximum values for efficiencies different to zero and the Carnot efficiency. Finally, analyzing the high temperature limit of AQHEs we discover the range of temperatures for which the quantum behaviour is valid.

DOI: 10.1515/jnet-2022-0081

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Journal of Non-Equilibrium Thermodynamics

Energy production in one-qubit quantum Agrawal machines

Julio J. Fernández

Published Jan 24, 2023• 20 citations

Publisher

Abstract

DOI: 10.1515/jnet-2022-0081

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β_{1}

and

β_{2}

(

<β_{1}

). In this processes, we obtain the work, heat, power and efficiency at maximum power output of the model. Our result of the efficiency at maximum power agree with the universal value in the first order of Carnot efficiency.

We study the efficiency at maximum power, ${\ensuremath{\eta}}_{m}$, of irreversible quantum Carnot engines (QCEs) that perform finite-time cycles between a hot and a cold reservoir at temperatures

{T}_{h}

and

{T}_{c}

, respectively. For QCEs in the reversible limit (long cycle period, zero dissipation), ${\ensuremath{\eta}}_{m}$ becomes identical to the Carnot efficiency ${\ensuremath{\eta}}_{{}_{C}}=1\ensuremath{-}{T}_{c}/{T}_{h}$. For QCE cycles in which nonadiabatic dissipation and the time spent on two adiabats are included, the efficiency ${\ensuremath{\eta}}_{m}$ at maximum power output is bounded from above by ${\ensuremath{\eta}}_{{}_{C}}/(2\ensuremath{-}{\ensuremath{\eta}}_{{}_{C}})$ and from below by ${\ensuremath{\eta}}_{{}_{C}}/2$. In the case of symmetric dissipation, the Curzon-Ahlborn efficiency ${\ensuremath{\eta}}_{{}_{\mathit{CA}}}=1\ensuremath{-}\sqrt{{T}_{c}/{T}_{h}}$ is recovered under the condition that the time allocation between the adiabats and the contact time with the reservoir satisfy a certain relation.