Maximum-Power Stirling-like Heat Engine with a Harmonically Confined Brownian Particle
Heat engines transform thermal energy into useful work, operating in a cyclic manner. For centuries, they have played a key role in industrial and technological development. Historically, only gases and liquids have been used as working substances, but the technical advances achieved in recent decad...
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MDPI AG
2025-01-01
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| Online Access: | https://www.mdpi.com/1099-4300/27/1/72 |
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| author | Irene Prieto-Rodríguez Antonio Prados Carlos A. Plata |
| author_facet | Irene Prieto-Rodríguez Antonio Prados Carlos A. Plata |
| author_sort | Irene Prieto-Rodríguez |
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| description | Heat engines transform thermal energy into useful work, operating in a cyclic manner. For centuries, they have played a key role in industrial and technological development. Historically, only gases and liquids have been used as working substances, but the technical advances achieved in recent decades allow for expanding the experimental possibilities and designing engines operating with a single particle. In this case, the system of interest cannot be addressed at a macroscopic level and their study is framed in the field of stochastic thermodynamics. In the present work, we study mesoscopic heat engines built with a Brownian particle submitted to harmonic confinement and immersed in a fluid acting as a thermal bath. We design a Stirling-like heat engine, composed of two isothermal and two isochoric branches, by controlling both the stiffness of the harmonic trap and the temperature of the bath. Specifically, we focus on the irreversible, non-quasi-static case—whose finite duration enables the engine to deliver a non-zero output power. This is a crucial aspect, which enables the optimisation of the thermodynamic cycle by maximising the delivered power—thereby addressing a key goal at the practical level. The optimal driving protocols are obtained by using both variational calculus and optimal control theory tools. Furthermore, we numerically explore the dependence of the maximum output power and the corresponding efficiency on the system parameters. |
| format | Article |
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| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-01-01 |
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| series | Entropy |
| spelling | doaj-art-ff8d7d050bd3470c9aef818814c821ad2025-01-24T13:31:53ZengMDPI AGEntropy1099-43002025-01-012717210.3390/e27010072Maximum-Power Stirling-like Heat Engine with a Harmonically Confined Brownian ParticleIrene Prieto-Rodríguez0Antonio Prados1Carlos A. Plata2Department of Physics, Ludwig-Maximilians-Universität München, Schellingstr. 4, D-80799 Munich, GermanyFísica Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Sevilla, SpainFísica Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Sevilla, SpainHeat engines transform thermal energy into useful work, operating in a cyclic manner. For centuries, they have played a key role in industrial and technological development. Historically, only gases and liquids have been used as working substances, but the technical advances achieved in recent decades allow for expanding the experimental possibilities and designing engines operating with a single particle. In this case, the system of interest cannot be addressed at a macroscopic level and their study is framed in the field of stochastic thermodynamics. In the present work, we study mesoscopic heat engines built with a Brownian particle submitted to harmonic confinement and immersed in a fluid acting as a thermal bath. We design a Stirling-like heat engine, composed of two isothermal and two isochoric branches, by controlling both the stiffness of the harmonic trap and the temperature of the bath. Specifically, we focus on the irreversible, non-quasi-static case—whose finite duration enables the engine to deliver a non-zero output power. This is a crucial aspect, which enables the optimisation of the thermodynamic cycle by maximising the delivered power—thereby addressing a key goal at the practical level. The optimal driving protocols are obtained by using both variational calculus and optimal control theory tools. Furthermore, we numerically explore the dependence of the maximum output power and the corresponding efficiency on the system parameters.https://www.mdpi.com/1099-4300/27/1/72Brownian heat engineoptimal power deliverystochastic thermodynamicsoptimal control theory |
| spellingShingle | Irene Prieto-Rodríguez Antonio Prados Carlos A. Plata Maximum-Power Stirling-like Heat Engine with a Harmonically Confined Brownian Particle Entropy Brownian heat engine optimal power delivery stochastic thermodynamics optimal control theory |
| title | Maximum-Power Stirling-like Heat Engine with a Harmonically Confined Brownian Particle |
| title_full | Maximum-Power Stirling-like Heat Engine with a Harmonically Confined Brownian Particle |
| title_fullStr | Maximum-Power Stirling-like Heat Engine with a Harmonically Confined Brownian Particle |
| title_full_unstemmed | Maximum-Power Stirling-like Heat Engine with a Harmonically Confined Brownian Particle |
| title_short | Maximum-Power Stirling-like Heat Engine with a Harmonically Confined Brownian Particle |
| title_sort | maximum power stirling like heat engine with a harmonically confined brownian particle |
| topic | Brownian heat engine optimal power delivery stochastic thermodynamics optimal control theory |
| url | https://www.mdpi.com/1099-4300/27/1/72 |
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