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Thermodynamic uncertainty relations in a linear system

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An Erratum to this article was published on 18 March 2020

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Abstract

We consider a Brownian particle in harmonic confinement of stiffness k, in one dimension in the underdamped regime. The whole setup is immersed in a heat bath at temperature T. The center of harmonic trap is dragged under any arbitrary protocol. The thermodynamic uncertainty relations for both position of the particle and current at time t are obtained using the second law of thermodynamics as well as the positive semi-definite property of the correlation matrix of work and degrees of freedom of the system for both underdamped and overdamped cases.

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  • 18 March 2020

    An error occurred during the proof correction step.

References

  1. U. Seifert, Eur. Phys. J. B 64, 423 (2008)

    ADS  Google Scholar 

  2. U. Seifert, Rep. Prog. Phys. 75, 126001 (2012)

    ADS  Google Scholar 

  3. K. Sekimoto, Progr. Theor. Phys. Suppl. 130, 17 (1998)

    ADS  Google Scholar 

  4. D.J. Evans, E.G.D. Cohen, G.P. Morriss, Phys. Rev. Lett. 71, 2401 (1993)

    ADS  Google Scholar 

  5. D.J. Evans, D.J. Searles, Phys. Rev. E 50, 1645 (1994)

    ADS  Google Scholar 

  6. G. Gallavotti, E.G.D. Cohen, Phys. Rev. Lett. 74, 2694 (1995)

    ADS  Google Scholar 

  7. G. Gallavotti, E.G.D. Cohen, J. Stat. Phys. 80, 931 (1995)

    ADS  Google Scholar 

  8. J. Kurchan, J. Phys. A: Math. General 31, 3719 (1998)

    ADS  Google Scholar 

  9. J.L. Lebowitz, H. Spohn, J. Stat. Phys. 95, 333 (1999)

    ADS  Google Scholar 

  10. D.J. Searles, D.J. Evans, J. Chem. Phys. 113, 3503 (2000)

    ADS  Google Scholar 

  11. D.J. Searles, D.J. Evans, Int. J. Thermophys. 22, 123 (2001)

    Google Scholar 

  12. C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)

    ADS  Google Scholar 

  13. G.E. Crooks, J. Stat. Phys. 90, 1481 (1998)

    ADS  Google Scholar 

  14. G.E. Crooks, Phys. Rev. E 60, 2721 (1999)

    ADS  Google Scholar 

  15. G.E. Crooks, Phys. Rev. E 61, 2361 (2000)

    ADS  Google Scholar 

  16. A.C. Barato, U. Seifert, Phys. Rev. Lett. 114, 158101 (2015)

    ADS  MathSciNet  Google Scholar 

  17. A.C. Barato, R. Chetrite, A. Faggionato, D. Gabrielli, New J. Phys. 20, 103023 (2018)

    Google Scholar 

  18. T. Koyuk, U. Seifert, P. Pietzonka, J. Phys. A: Math. Theor. 52, 02LT02 (2018)

    Google Scholar 

  19. A.C. Barato, U. Seifert, J. Phys. Chem. B 119, 6555 (2015)

    Google Scholar 

  20. A.C. Barato, U. Seifert, Phys. Rev. X 6, 041053 (2016)

    Google Scholar 

  21. J.M. Horowitz, T.R. Gingrich, Phys. Rev. E 96, 020103 (2017)

    ADS  Google Scholar 

  22. C. Maes, Phys. Rev. Lett. 119, 160601 (2017)

    ADS  Google Scholar 

  23. S.K. Manikandan, S. Krishnamurthy, J. Phys. A: Math. Theor. 51, 11LT01 (2018)

    Google Scholar 

  24. P. Pietzonka, F. Ritort, U. Seifert, Phys. Rev. E 96, 012101 (2017)

    ADS  Google Scholar 

  25. S. Pigolotti, I. Neri, E. Roldán, F. Jülicher, Phys. Rev. Lett. 119, 140604 (2017)

    ADS  Google Scholar 

  26. J.P. Garrahan, Phys. Rev. E 95, 032134 (2017)

    ADS  Google Scholar 

  27. A.C. Barato, U. Seifert, Phys. Rev. E 92, 032127 (2015)

    ADS  Google Scholar 

  28. T.R. Gingrich, J.M. Horowitz, N. Perunov, J.L. England, Phys. Rev. Lett. 116, 120601 (2016)

    ADS  Google Scholar 

  29. H. Touchette, Phys. Rep. 478, 1 (2009)

    ADS  MathSciNet  Google Scholar 

  30. M. Polettini, A. Lazarescu, M. Esposito, Phys. Rev. E 94, 052104 (2016)

    ADS  Google Scholar 

  31. P. Pietzonka, A.C. Barato, U. Seifert, Phys. Rev. E 93, 052145 (2016)

    ADS  Google Scholar 

  32. N. Shiraishi, Finite-time thermodynamic uncertainty relation do not hold for discrete-time Markov process, https://arXiv:1706.00892 (2017)

  33. K. Proesmans, C.V. den Broeck, Europhys. Lett. 119, 20001 (2017)

    ADS  Google Scholar 

  34. D. Chiuchiù, S. Pigolotti, Phys. Rev. E 97, 032109 (2018)

    ADS  MathSciNet  Google Scholar 

  35. I.D. Terlizzi, M. Baiesi, J. Phys. A: Math. Theor. 52, 02LT03 (2018)

    Google Scholar 

  36. A. Dechant, J. Phys. A: Math. Theor. 52, 035001 (2018)

    ADS  MathSciNet  Google Scholar 

  37. C. Hyeon, W. Hwang, Phys. Rev. E 96, 012156 (2017)

    ADS  Google Scholar 

  38. A. Dechant, S. Ichi Sasa, J. Stat. Mech. Theory Exp. 2018, 063209 (2018)

    Google Scholar 

  39. W. Hwang, C. Hyeon, J. Phys. Chem. Lett. 9, 513 (2018)

    Google Scholar 

  40. R. Harris, M. Shreshtha, Europhys. Lett. 126, 40007 (2019)

    Google Scholar 

  41. R. Marsland III, W. Cui, J.M. Horowitz, J. R. Soc. Interface 16, 20190098 (2019)

    Google Scholar 

  42. S. Lee, C. Hyeon, J. Jo, Phys. Rev. E 98, 032119 (2018)

    ADS  Google Scholar 

  43. H.-M. Chun, L.P. Fischer, U. Seifert, Phys. Rev. E 99, 042128 (2019)

    ADS  Google Scholar 

  44. K. Macieszczak, K. Brandner, J.P. Garrahan, Phys. Rev. Lett. 121, 130601 (2018)

    ADS  Google Scholar 

  45. T. Van Vu, Y. Hasegawa, J. Phys. A: Math. Theor. 53, 075001 (2020)

    ADS  Google Scholar 

  46. Y. Hasegawa, T. Van Vu, Phys. Rev. E 99, 062126 (2019)

    ADS  Google Scholar 

  47. T. Van Vu, Y. Hasegawa, Phys. Rev. E 100, 032130 (2019)

    ADS  MathSciNet  Google Scholar 

  48. T. Van Vu, Y. Hasegawa, Phys. Rev. E 100, 012134 (2019)

    ADS  Google Scholar 

  49. A. Barato, R. Chetrite, A. Faggionato, D. Gabrielli, J. Stat. Mech.: Theory Exp. 2019, 084017 (2019)

    Google Scholar 

  50. Y. Hasegawa, T. Van Vu, Phys. Rev. Lett. 123, 110602 (2019)

    ADS  MathSciNet  Google Scholar 

  51. P.P. Potts, P. Samuelsson, Phys. Rev. E 100, 052137 (2019)

    ADS  Google Scholar 

  52. K. Proesmans, J.M. Horowitz, J. Stat. Mech.: Theory Exp. 2019, 054005 (2019)

    Google Scholar 

  53. U. Seifert, Phys. Rev. Lett. 95, 040602 (2005)

    ADS  Google Scholar 

  54. G.M. Wang, J.C. Reid, D.M. Carberry, D.R.M. Williams, E.M. Sevick, D.J. Evans, Phys. Rev. E 71, 046142 (2005)

    ADS  Google Scholar 

  55. G.M. Wang, E.M. Sevick, E. Mittag, D.J. Searles, D.J. Evans, Phys. Rev. Lett. 89, 050601 (2002)

    ADS  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Fisica ‘G. Galilei’, INFN, Università di Padova, Via Marzolo 8, 35131, Padova, Italy

    Deepak Gupta & Amos Maritan

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  1. Deepak Gupta
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  2. Amos Maritan
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Correspondence to Deepak Gupta.

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Gupta, D., Maritan, A. Thermodynamic uncertainty relations in a linear system. Eur. Phys. J. B 93, 28 (2020). https://doi.org/10.1140/epjb/e2020-10019-4

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  • DOI: https://doi.org/10.1140/epjb/e2020-10019-4

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