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Nonequilibrium fluctuation-response relations for state-current correlations

Krzysztof Ptaszyński1,*, Timur Aslyamov2,†, and Massimiliano Esposito2,‡

  • *Contact author: krzysztof.ptaszynski@ifmpan.poznan.pl
  • †Contact author: timur.aslyamov@uni.lu
  • ‡Contact author: massimiliano.esposito@uni.lu
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Phys. Rev. E 113, 024131 – Published 20 February, 2026

DOI: https://doi.org/10.1103/4htr-dfc5

Abstract

Recently, exact identities known as fluctuation-response relations (FRRs) have been derived for nonequilibrium steady states of Markov jump processes. These identities link the fluctuations of state or current observables to a combination of responses of these observables to perturbations of transition rates. Here, we complement these results by deriving analogous FRRs applicable to mixed covariances of one state and one current observable. We further derive inverse FRRs expressing individual state or current response in terms of a combination of covariances rather than vice versa. Using these relations, we demonstrate that the breaking of the Onsager symmetry requires the presence of state-current correlations. On the practical side, we demonstrate the applicability of FRRs for explaining the behavior of fluctuations in quantum dot devices or enzymatic reaction networks.

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Nonequilibrium fluctuation-response relations for state observables

Krzysztof Ptaszyński, Timur Aslyamov, and Massimiliano Esposito
Phys. Rev. E 113, 024130 (2026)

Article Text

References (104)

  1. K. Ptaszyński, T. Aslyamov, and M. Esposito, preceding paper, Phys. Rev. E 113, 024130 (2026).
  2. T. Aslyamov, K. Ptaszyński, and M. Esposito, Phys. Rev. Lett. 134, 157101 (2025).
  3. Y. Utsumi, Phys. Rev. B 75, 035333 (2007).
  4. Y. Utsumi, Physica E 40, 355 (2007).
  5. Y. Utsumi, D. S. Golubev, and G. Schön, Phys. Status Solidi C 5, 154 (2008).
  6. C. Dieball and A. Godec, J. Phys. A: Math. Theor. 55, 475001 (2022).
  7. R. Kubo, Rep. Prog. Phys. 29, 255 (1966).
  8. R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II: Nonequilibrium Statistical Mechanics, Vol. 31 (Springer Science & Business Media, Cham, 2012).
  9. R. L. Stratonovich, Nonlinear Nonequilibrium Thermodynamics I: Linear and Nonlinear Fluctuation-Dissipation Theorems, Vol. 57 (Springer Science & Business Media, Cham, 2012).
  10. U. M. B. Marconi, A. Puglisi, L. Rondoni, and A. Vulpiani, Phys. Rep. 461, 111 (2008).
  11. D. Forastiere, R. Rao, and M. Esposito, New J. Phys. 24, 083021 (2022).
  12. G. S. Agarwal, Z. Phys. A: At. Nucl. 252, 25 (1972).
  13. M. Baiesi, C. Maes, and B. Wynants, Phys. Rev. Lett. 103, 010602 (2009).
  14. U. Seifert and T. Speck, Europhys. Lett. 89, 10007 (2010).
  15. J. Prost, J.-F. Joanny, and J. M. R. Parrondo, Phys. Rev. Lett. 103, 090601 (2009).
  16. B. Altaner, M. Polettini, and M. Esposito, Phys. Rev. Lett. 117, 180601 (2016).
  17. C. Maes, Front. Phys. 8, 229 (2020).
  18. H.-M. Chun and J. M. Horowitz, J. Chem. Phys. 158, 174115 (2023).
  19. N. Shiraishi, An Introduction to Stochastic Thermodynamics, Fundamental Theories of Physics (Springer, Singapore, 2023).
  20. Q. Gao, H.-M. Chun, and J. M. Horowitz, Europhys. Lett. 146, 31001 (2024).
  21. L. Tesser and J. Splettstoesser, Phys. Rev. Lett. 132, 186304 (2024).
  22. C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997).
  23. G. E. Crooks, Phys. Rev. E 60, 2721 (1999).
  24. M. Esposito, U. Harbola, and S. Mukamel, Rev. Mod. Phys. 81, 1665 (2009).
  25. U. Seifert, Rep. Prog. Phys. 75, 126001 (2012).
  26. A. C. Barato and U. Seifert, Phys. Rev. Lett. 114, 158101 (2015).
  27. T. R. Gingrich, J. M. Horowitz, N. Perunov, and J. L. England, Phys. Rev. Lett. 116, 120601 (2016).
  28. P. Pietzonka, A. C. Barato, and U. Seifert, Phys. Rev. E 93, 052145 (2016).
  29. P. Pietzonka, F. Ritort, and U. Seifert, Phys. Rev. E 96, 012101 (2017).
  30. J. M. Horowitz and T. R. Gingrich, Phys. Rev. E 96, 020103(R) (2017).
  31. G. Falasco, M. Esposito, and J.-C. Delvenne, New J. Phys. 22, 053046 (2020).
  32. J. M. Horowitz and T. R. Gingrich, Nat. Phys. 16, 15 (2020).
  33. T. Van Vu, V. Tuan Vo, and Y. Hasegawa, Phys. Rev. E 101, 042138 (2020).
  34. T. Van Vu and K. Saito, Phys. Rev. X 13, 011013 (2023).
  35. I. Di Terlizzi and M. Baiesi, J. Phys. A: Math. Theor. 52, 02LT03 (2019).
  36. N. Shiraishi, J. Stat. Phys. 185, 19 (2021).
  37. V. Lucarini, J. Stat. Phys. 162, 312 (2016).
  38. M. Santos Gutiérrez and V. Lucarini, J. Stat. Phys. 179, 1572 (2020).
  39. G. Falasco, T. Cossetto, E. Penocchio, and M. Esposito, New J. Phys. 21, 073005 (2019).
  40. J. D. Mallory, A. B. Kolomeisky, and O. A. Igoshin, Proc. Natl. Acad. Sci. USA 117, 8884 (2020).
  41. J. A. Owen, T. R. Gingrich, and J. M. Horowitz, Phys. Rev. X 10, 011066 (2020).
  42. J. A. Owen and J. M. Horowitz, Nat. Commun. 14, 1280 (2023).
  43. G. Fernandes Martins and J. M. Horowitz, Phys. Rev. E 108, 044113 (2023).
  44. T. Aslyamov and M. Esposito, Phys. Rev. Lett. 132, 037101 (2024).
  45. T. Aslyamov and M. Esposito, Phys. Rev. Lett. 133, 107103 (2024).
  46. P. E. Harunari, S. Dal Cengio, V. Lecomte, and M. Polettini, Phys. Rev. Lett. 133, 047401 (2024).
  47. S. D. Cengio, P. E. Harunari, V. Lecomte, and M. Polettini, SciPost Phys. 19, 111 (2025).
  48. F. Khodabandehlou, C. Maes, and K. Netočny, J. Phys. A: Math. Theor. 58, 155002 (2025).
  49. C. Floyd, A. R. Dinner, and S. Vaikuntanathan, arXiv:2404.03798.
  50. D. Frezzato, J. Chem. Phys. 160, 234111 (2024).
  51. C. Floyd, A. R. Dinner, A. Murugan, and S. Vaikuntanathan, Nat. Commun. 16, 7184 (2025).
  52. Q. Gao, H.-M. Chun, and J. M. Horowitz, Phys. Rev. E 105, L012102 (2022).
  53. R. Bao and S. Liang, arXiv:2412.19602.
  54. J. Zheng and Z. Lu, Phys. Rev. E 112, 064103 (2025).
  55. A. Dechant and S. I. Sasa, arXiv:1804.08250.
  56. A. Dechant and S.-I. Sasa, Proc. Natl. Acad. Sci. USA 117, 6430 (2020).
  57. G. Falasco, M. Esposito, and J.-C. Delvenne, J. Phys. A: Math. Theor. 55, 124002 (2022).
  58. T. Monnai, Phys. Rev. E 110, L062101 (2024).
  59. J. Zheng and Z. Lu, Phys. Rev. E 112, L012103 (2025).
  60. K. Ptaszyński, T. Aslyamov, and M. Esposito, Phys. Rev. Lett. 133, 227101 (2024).
  61. K. Liu and J. Gu, Commun. Phys. 8, 62 (2025).
  62. E. Kwon, H.-M. Chun, H. Park, and J. S. Lee, Phys. Rev. Lett. 135, 097101 (2025).
  63. T. Van Vu, PRX Quantum 6, 010343 (2025).
  64. K. Liu and J. Gu, arXiv:2501.04895.
  65. G. Bakewell-Smith, F. Girotti, M. Guţă, and J. P. Garrahan, Phys. Rev. Lett. 131, 197101 (2023).
  66. P. Pietzonka and F. Coghi, Phys. Rev. E 109, 064128 (2024).
  67. A. Wachtel, R. Rao, and M. Esposito, New J. Phys. 20, 042002 (2018).
  68. T. Ritz, S. Adem, and K. Schulten, Biophys. J. 78, 707 (2000).
  69. P. J. Hore and H. Mouritsen, Annu. Rev. Biophys. 45, 299 (2016).
  70. R. Wiltschko and W. Wiltschko, J. R. Soc. Interface. 16, 20190295 (2019).
  71. H. Zadeh-Haghighi and C. Simon, J. R. Soc. Interface. 19, 20220325 (2022).
  72. S. Gustavsson, R. Leturcq, B. Simovič, R. Schleser, T. Ihn, P. Studerus, K. Ensslin, D. C. Driscoll, and A. C. Gossard, Phys. Rev. Lett. 96, 076605 (2006).
  73. S. Gustavsson, R. Leturcq, M. Studer, I. Shorubalko, T. Ihn, K. Ensslin, D. Driscoll, and A. Gossard, Surf. Sci. Rep. 64, 191 (2009).
  74. R. Sánchez, P. Samuelsson, and P. P. Potts, Phys. Rev. Res. 1, 033066 (2019).
  75. N. Freitas, J.-C. Delvenne, and M. Esposito, Phys. Rev. X 11, 031064 (2021).
  76. A. Gopal, M. Esposito, and N. Freitas, Phys. Rev. B 106, 155303 (2022).
  77. R. Rao and M. Esposito, New J. Phys. 20, 023007 (2018).
  78. G. Falasco and M. Esposito, Rev. Mod. Phys. 97, 015002 (2025).
  79. M. Drazin, Am. Math. Mon. 65, 506 (1958).
  80. G. E. Crooks, On the Drazin inverse of the rate matrix, Technical note (2018), https://threeplusone.com/pubs/on_drazin.pdf.
  81. G. T. Landi, M. J. Kewming, M. T. Mitchison, and P. P. Potts, PRX Quantum 5, 020201 (2024).
  82. S. E. Harvey, S. Lahiri, and S. Ganguli, Phys. Rev. E 108, 014403 (2023).
  83. A. Lapolla and A. Godec, New J. Phys. 20, 113021 (2018).
  84. A. Lapolla and A. Godec, Front. Phys. 7, 182 (2019).
  85. A. Lapolla, D. Hartich, and A. Godec, Phys. Rev. Res. 2, 043084 (2020).
  86. K. Ptaszyński and M. Esposito, Phys. Rev. E 111, 034125 (2025).
  87. A. Wachtel, J. Vollmer, and B. Altaner, Phys. Rev. E 92, 042132 (2015).
  88. M. Bruderer, L. D. Contreras-Pulido, M. Thaller, L. Sironi, D. Obreschkow, and M. B. Plenio, New J. Phys. 16, 033030 (2014).
  89. A. C. Barato and U. Seifert, Phys. Rev. Lett. 115, 188103 (2015).
  90. W. Ledermann and G. E. H. Reuter, Philos. Trans. R. Soc. A 246, 321 (1954).
  91. F. Schlögl, Z. Phys. 253, 147 (1972).
  92. M. Vellela and H. Qian, J. R. Soc. Interface. 6, 925 (2009).
  93. H. Ge and H. Qian, Phys. Rev. Lett. 103, 148103 (2009).
  94. R. Landauer, J. App. Phys. 33, 2209 (1962).
  95. P. Hänggi and H. Thomas, Phys. Rep. 88, 207 (1982).
  96. T. Herpich, T. Cossetto, G. Falasco, and M. Esposito, New J. Phys. 22, 063005 (2020).
  97. J. Meibohm and M. Esposito, Phys. Rev. Lett. 128, 110603 (2022).
  98. J. Meibohm and M. Esposito, New J. Phys. 25, 023034 (2023).
  99. H. Vroylandt, M. Esposito, and G. Verley, Europhys. Lett. 120, 30009 (2017).
  100. H. Vroylandt, M. Esposito, and G. Verley, Phys. Rev. Lett. 124, 250603 (2020).
  101. G. T. Nieddu, E. Forgoston, and L. Billings, J. R. Soc., Interface 19, 20220253 (2022).
  102. E. Lerner, T. Cordes, A. Ingargiola, Y. Alhadid, S. Chung, X. Michalet, and S. Weiss, Science 359, eaan1133 (2018).
  103. B. P. English, W. Min, A. M. Van Oijen, K. T. Lee, G. Luo, H. Sun, B. J. Cherayil, S. Kou, and X. S. Xie, Nat. Chem. Biol. 2, 87 (2006).
  104. K. Ptaszyński, T. Aslyamov, and M. Esposito, Nonequilibrium fluctuation-response relations for state-current correlations, Zenodo (2026), doi:10.5281/zenodo.18560924.

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Information

Phys. Rev. E 113, 024131– Published 20 February, 2026
  • Received 12 June 2025
  • Revised 19 December 2025
  • Accepted 27 January 2026
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