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Non-Markovian entropy production fluctuation theorem driven by a time-dependent electric field

K. S. Rodríguez-Vigil, M. A. Bastarrachea-Magnani, and J. I. Jiménez-Aquino

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Phys. Rev. E 114, 044122 – Published 15 October, 2026

DOI: https://doi.org/10.1103/sy8c-3wkn

Abstract

Fluctuation theorems are key to understanding both fundamental and applied aspects of nonequilibrium thermodynamics of small systems. We study the non-Markovian entropy production fluctuation theorem for the diffusion process of charged particles in a gas inside a harmonic potential and under the action of a time-dependent electric field, using a generalized Langevin equation. By considering the influence of the electric field on both the tagged Brownian particle and the bath particles, an “induced” electric force arises. Despite the additional force, we demonstrate that Kubo's second fluctuation-dissipation theorem (FDT) remains unchanged. The FDT allows us to obtain the Gaussian probability density for the position along a single stochastic trajectory, which is the key to demonstrating the validity of the detailed fluctuation theorem for the total entropy production. We study the specific result of an Ornstein-Uhlenbeck-type friction memory kernel and an oscillating electric field, and analyze the average work and entropy production in different parameter regimes.

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References (41)

  1. G. N. Bochkov and Yu. E. Kuzovlev, Nonlinear fluctuation-dissipation relations and stochastic models in nonequilibrium thermodynamics: I. Generalized fluctuation-dissipation theorem, Phys. A 106, 443 (1981).
  2. D. J. Evans, E. G. D. Cohen, and G. P. Morriss, Probability of second law violations in shearing steady states, Phys. Rev. Lett. 71, 2401 (1993).
  3. G. Gallavotti and E. G. D. Cohen, Dynamical ensembles in nonequilibrium statistical mechanics, Phys. Rev. Lett. 74, 2694 (1995).
  4. C. Jarzynski, Equilibrium free-energy differences from nonequilibrium measurements: A master-equation approach, Phys. Rev. E 56, 5018 (1997).
  5. G. E. Crooks, Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences, Phys. Rev. E 60, 2721 (1999).
  6. J. Kurchan, Fluctuation theorem for stochastic dynamics, J. Phys. A: Math. Gen. 31, 3719 (1998).
  7. R. van Zon, S. Ciliberto, and E. G. D. Cohen, Power and heat fluctuation theorem for electric circuit, Phys. Rev. Lett. 92, 130601 (2004).
  8. J. D. Noh and J.-M. Park, Fluctuation relation for heat, Phys. Rev. Lett. 108, 240603 (2012).
  9. J. I. Jiménez-Aquino and R. M. Velasco, Power fluctuation theorem for a Brownian harmonic oscillator, Phys. Rev. E 87, 022112 (2013).
  10. R. Rao and M. Esposito, Detailed fluctuation theorems: A unifying perspective, Entropy 20, 635 (2018).
  11. J. J. Park and H. Nha, Fluctuation theorem for information thermodynamics of quantum correlated systems, Entropy 25, 165, (2023).
  12. M. Semeraro, A. Suma, and G. Negro, Fluctuation theorems for heat exchanges between passive and active baths, Entropy 26, 439 (2024).
  13. K. Funo, M. Ueda, and T. Sagawa, Quantum fluctuation theorems, in Thermodynamics in the Quantum Regime. Fundamental Theories of Physics, edited by F. Binder, L. Correa, C. Gogolin, J. Anders, and G. Adesso (Springer, Cham, 2018), Vol 195, pp. 249–273.
  14. F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso, Thermodynamics in the Quantum Regime (Springer, Cham, 2018), Vol. 195.
  15. K. Hayashi, Application of the fluctuation theorem to motor proteins: From F1-ATPase to axonal cargo transport by kinesin and dynein, Biophys. Rev. 10, 1311 (2018).
  16. S. Chaki and R. Chakrabarti, Entropy production and work fluctuation relations for a single particle in active bath, Phys. A 511, 302 (2018).
  17. K. Goswami, Work fluctuation relations for a dragged Brownian particle in active bath, Phys. A 525, 223 (2019).
  18. N. Narinder, S. Paul, and C. Bechinger, Work fluctuation relation of an active Brownian particle in a viscoelastic fluid, Phys. Rev. E 104, 034605 (2021).
  19. A. Argun, A.-R. Moradi, E. Pince, G. B. Bagci, and G. Volpe, Experimental evidence of the failure of Jarzynski equality in active baths, arXiv:1601.01123.
  20. B. Mahault, E. Tang, and R. Golestanian, A topological fluctuation theorem, Nat. Commun. 13, 3036 (2022).
  21. Q. Zeng and J. Wang, New fluctuation theorems on Maxwell's demon, Sci. Adv. 7, eabf1807 (2021).
  22. P. Hack, C. Lindig-Leon, S. Gottwald, and D. A. Braun, Thermodynamic fluctuation theorems govern human sensorimotor learning, Sci. Rep. 13, 869 (2023).
  23. P. Sidajaya, J. H. K. Low, C. C. Aw, and V. Scarani, Emergence of fluctuation relations in UNO, Phys. Rev. Res. 7, 023054 (2025).
  24. U. Seifert, Entropy production along a stochastic trajectory and an integral fluctuation theorem, Phys. Rev. Lett. 95, 040602 (2005).
  25. A. Saha, S. Lahiri, and A. M. Jayannavar, Entropy production and fluctuation theorems in driven mesoscopic systems, Phys. Rev. E 80, 011117 (2009).
  26. J. I. Jiménez-Aquino, Entropy production theorem for a charged particle in an electromagnetic field, Phys. Rev. E 82, 051118 (2010).
  27. T. Mai and A. Dhar, Nonequilibrium work fluctuations for oscillators in non-Markovian baths, Phys. Rev. E 75, 061101 (2007).
  28. T. Ohkuma and T. Ohta, Fluctuation theorems for non-linear generalized Langevin systems, J. Stat. Mech. (2007) P10010.
  29. J. I. Jiménez-Aquino, Non-Markovian work fluctuation theorem in crossed electric and magnetic fields, Phys. Rev. E 92, 022149 (2015).
  30. B. Ghosh and S. Chaudhury, Fluctuation theorems for total entropy production in generalized Langevin systems, Phys. A 466, 133 (2017).
  31. B. Cui and A. Zaccone, Generalized Langevin equation and fluctuation-dissipation theorem for particle-bath systems in external oscillating fields, Phys. Rev. E 97, 060102(R) (2018).
  32. R. Zwanzig, Nonequilibrium Statistical Mechanics (Oxford University Press, New York, 2001).
  33. J. F. García-Camacho, O. Contreras-Vergara, N. Sánchez-Salas, G. A. de Parga, and J. I. Jiménez-Aquino, Validity of Kubo's fluctuation–dissipation theorem in systems driven by a time-dependent electric field, Phys. A 674, 130692 (2025).
  34. J. Tóthová, A. Šoltýs, and V. Lisý, Brownian motion in a bath responding to external electric fields, J. Mol. Liq. 317, 113920 (2020).
  35. V. Lisý and J. Tóthová, Generalized Langevin equation and the fluctuation-dissipation theorem for particle-bath systems in a harmonic field, Results Phys. 12, 1212 (2019).
  36. K. Sekimoto, Stochastic Energetics, Lecture Notes in Physics Vol. 799 (Springer, Heidelberg, 2010).
  37. J. Łuczka, Non-Markovian stochastic processes: Colored noise, Chaos 15, 026107 (2005).
  38. L. Ferrari, Test particles in a gas: Markovian and non-Markovian Langevin dynamics, Chem. Phys. 523, 42 (2019).
  39. L. Ferrari, Particles dispersed in a dilute gas: Limits of validity of the Langevin equation, Chem. Phys. 336, 27 (2007).
  40. L. Ferrari, Erratum to “Particles dispersed in a dilute gas: Limits of validity of the Langevin equation”, Chem. Phys. 337, 177 (2007).
  41. K. S. Rodríguez-Vigil, M. A. Bastarrachea-Magnani, and J. I. Jiménez-Aquino, Data for Non-Markovian entropy production fluctuation theorem driven by a time-dependent electric field (Version 1.0) [Data set], Zenodo, 2026, https://doi.org/10.5281/zenodo.21665170.

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Phys. Rev. E 114, 044122– Published 15 October, 2026
  • Received 4 May 2026
  • Accepted 9 September 2026
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