Abstract.
We study a Brownian Carnot cycle introduced by Schmiedl and Seifert [Europhys. Lett. 81, 20003 (2008)] from a viewpoint of the linear irreversible thermodynamics. By considering the entropy production rate of this cycle, we can determine thermodynamic forces and fluxes of the cycle and calculate the Onsager coefficients for general protocols, that is, arbitrary schedules to change the potential confining the Brownian particle. We show that these Onsager coefficients contain the information of the protocol shape and they satisfy the tight-coupling condition irrespective of whatever protocol shape we choose. These properties may give an explanation why the Curzon-Ahlborn efficiency often appears in the finite-time heat engines.
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References
F. Curzon, B. Ahlborn, Am. J. Phys. 43, 22 (1975)
H. Callen, Thermodynamics and an Introduction to Thermostatistics (Wiley, New York, 1985), 2nd edn., Chap. 4
I.I. Novikov, J. Nuclear Energy II 7, 125 (1958)
M.H. Rubin, Phys. Rev. A 19, 1272 (1979)
M.H. Rubin, Phys. Rev. A 19, 1277 (1979)
P.T. Landsberg, H. Leff, J. Phys. A 22, 4019 (1989)
J.M. Gordon, Am. J. Phys. 57, 1136 (1989)
R. Kosloff, J. Chem. Phys. 80, 1625 (1984)
A. Benjamin, J. Appl. Phys. 79, 1191 (1996)
M. Asfaw, M. Bekele, Eur. Phys. J. B 38, 457 (2004)
M. Asfaw, M. Bekele, Phys. Rev. E 72, 056109 (2005)
C. Van den Broeck, Phys. Rev. Lett. 95, 190602 (2005)
B. Jiménez de Cisneros, A. Calvo Hernández, Phys. Rev. Lett. 98, 130602 (2007)
B. Jiménez de Cisneros, A. Calvo Hernández, Phys. Rev. E 77, 041127 (2008)
A. Gomez-Marin, J.M. Sancho, Phys. Rev. E 74, 062102 (2006)
R. Benjamin, R. Kawai, Phys. Rev. E 77, 051132 (2008)
M. Van den Broeck, C. Van den Broeck, Phys. Rev. Lett. 100, 130601 (2008)
T. Gao, Y. Zhang, J. Chen, Chinese Phys. B. 18, 3279 (2009)
R. Rutten, M. Esposito, B. Cleuren, Phys. Rev. B 80, 235112 (2009)
R. Benjamin, arXiv: 0907.0829v1
Y. Izumida, K. Okuda, Europhys. Lett. 83, 60003 (2008)
Y. Izumida, K. Okuda, Prog. Theor. Phys. Suppl. 178, 163 (2009)
Y. Izumida, K. Okuda, Phys. Rev. E 80, 021121 (2009)
T. Schmiedl, U. Seifert, Europhys. Lett. 81, 20003 (2008)
Z.C. Tu, J. Phys. A. 41, 312003 (2008)
M. Esposito, K. Lindenberg, C. Van den Broeck, Europhys. Lett. 85, 60010 (2009)
M. Esposito, K. Lindenberg, C. Van den Broeck, Phys. Rev. Lett. 102, 130602 (2009)
J. Birjukov, T. Jahnke, G. Mahler, Eur. Phys. J. B 64, 105 (2008)
A.E. Allahverdyan, R.S. Johal, G. Mahler, Phys. Rev. E 77, 041118 (2008)
R.S. Johal, Phys. Rev. E 80, 041119 (2009)
M. Esposito, R. Kawai, K. Lindenberg, C. Van den Broeck, Phys. Rev. E 81, 041106 (2010)
Y. Zhou, D. Segal, Phys. Rev. E 82, 011120 (2010)
L. Onsager, Phys. Rev. 37, 405 (1931)
S.R. de Groot, P. Mazur, Non-Equilibrium Thermodynamics (Dover, New York, 1984)
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Izumida, Y., Okuda, K. Onsager coefficients of a Brownian Carnot cycle. Eur. Phys. J. B 77, 499–504 (2010). https://doi.org/10.1140/epjb/e2010-00285-0
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DOI: https://doi.org/10.1140/epjb/e2010-00285-0