Thermodynamics of two-stroke engine based on periodically driven two-level system

Proceedings of the international conference Frontiers of Quantum and Mesoscopic Thermodynamics FQMT '08

Petr Chvosta, Viktor Holubec, Artem Ryabov, Mario Einax, Philipp Maass

Research output: Contribution to journalArticle

Abstract

We investigate a microscopic motor based on an externally driven two-level system. One cycle of the motor operation consists of two strokes. Within each stroke, the two energy levels are driven with a constant rate. The occupation probabilities of the two states evolve according to the Pauli rate equation and represent the delayed system's response to the external driving. We give the exact solution of the Pauli rate equation and discuss its thermodynamical consequences. In particular, we calculate the motor's efficiency, the power output, and the performance dependence on the control parameters. Secondly, we introduce an augmented stochastic process which reflects, at a given time, both the occupation probabilities for the two states and the time spent in the individual states during the previous evolution. Our exact calculation of the evolution operator for the augmented process allows one to discuss in detail the probability density for the work during the limit cycle. In the strongly irreversible regime, the density shows strong deviations from a Gaussian shape.
Original languageEnglish
Pages (from-to)472-476
Number of pages5
JournalPhysica E: Low-Dimensional Systems and Nanostructures
Volume42
Issue number3
DOIs
Publication statusPublished - 2010

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Thermodynamics
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Random processes
Electron energy levels
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Cite this

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title = "Thermodynamics of two-stroke engine based on periodically driven two-level system: Proceedings of the international conference Frontiers of Quantum and Mesoscopic Thermodynamics FQMT '08",
abstract = "We investigate a microscopic motor based on an externally driven two-level system. One cycle of the motor operation consists of two strokes. Within each stroke, the two energy levels are driven with a constant rate. The occupation probabilities of the two states evolve according to the Pauli rate equation and represent the delayed system's response to the external driving. We give the exact solution of the Pauli rate equation and discuss its thermodynamical consequences. In particular, we calculate the motor's efficiency, the power output, and the performance dependence on the control parameters. Secondly, we introduce an augmented stochastic process which reflects, at a given time, both the occupation probabilities for the two states and the time spent in the individual states during the previous evolution. Our exact calculation of the evolution operator for the augmented process allows one to discuss in detail the probability density for the work during the limit cycle. In the strongly irreversible regime, the density shows strong deviations from a Gaussian shape.",
author = "Petr Chvosta and Viktor Holubec and Artem Ryabov and Mario Einax and Philipp Maass",
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TY - JOUR

T1 - Thermodynamics of two-stroke engine based on periodically driven two-level system

T2 - Proceedings of the international conference Frontiers of Quantum and Mesoscopic Thermodynamics FQMT '08

AU - Chvosta, Petr

AU - Holubec, Viktor

AU - Ryabov, Artem

AU - Einax, Mario

AU - Maass, Philipp

PY - 2010

Y1 - 2010

N2 - We investigate a microscopic motor based on an externally driven two-level system. One cycle of the motor operation consists of two strokes. Within each stroke, the two energy levels are driven with a constant rate. The occupation probabilities of the two states evolve according to the Pauli rate equation and represent the delayed system's response to the external driving. We give the exact solution of the Pauli rate equation and discuss its thermodynamical consequences. In particular, we calculate the motor's efficiency, the power output, and the performance dependence on the control parameters. Secondly, we introduce an augmented stochastic process which reflects, at a given time, both the occupation probabilities for the two states and the time spent in the individual states during the previous evolution. Our exact calculation of the evolution operator for the augmented process allows one to discuss in detail the probability density for the work during the limit cycle. In the strongly irreversible regime, the density shows strong deviations from a Gaussian shape.

AB - We investigate a microscopic motor based on an externally driven two-level system. One cycle of the motor operation consists of two strokes. Within each stroke, the two energy levels are driven with a constant rate. The occupation probabilities of the two states evolve according to the Pauli rate equation and represent the delayed system's response to the external driving. We give the exact solution of the Pauli rate equation and discuss its thermodynamical consequences. In particular, we calculate the motor's efficiency, the power output, and the performance dependence on the control parameters. Secondly, we introduce an augmented stochastic process which reflects, at a given time, both the occupation probabilities for the two states and the time spent in the individual states during the previous evolution. Our exact calculation of the evolution operator for the augmented process allows one to discuss in detail the probability density for the work during the limit cycle. In the strongly irreversible regime, the density shows strong deviations from a Gaussian shape.

U2 - 10.1016/j.physe.2009.06.031

DO - 10.1016/j.physe.2009.06.031

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EP - 476

JO - Physica E: Low-Dimensional Systems and Nanostructures

JF - Physica E: Low-Dimensional Systems and Nanostructures

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