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arxiv: 2605.03191 · v1 · submitted 2026-05-04 · ❄️ cond-mat.stat-mech

Recognition: unknown

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

J. I. Jim\'enez-Aquino, K. S. Rodr\'iguez-Vigil, M. A. Bastarrachea-Magnani

Authors on Pith no claims yet

Pith reviewed 2026-05-08 17:10 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech
keywords fluctuation theoremsnon-Markovian dynamicsentropy productiongeneralized Langevin equationelectric fieldBrownian motionfluctuation-dissipation theorem
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The pith

Despite an induced electric force, Kubo's second fluctuation-dissipation theorem stays the same, enabling the detailed fluctuation theorem for entropy production.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper examines non-Markovian diffusion of charged particles in a harmonic trap under a time-dependent electric field using a generalized Langevin equation. The field acts on both the particle and the bath, creating an induced force, yet the authors show that Kubo's second fluctuation-dissipation theorem is unaffected. This invariance keeps the position distribution Gaussian for each trajectory. The Gaussian statistics then allow proof that the detailed fluctuation theorem holds for the total entropy production. Readers interested in small-system thermodynamics would care because it extends fluctuation theorems to driven non-Markovian cases without new corrections.

Core claim

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 (DFT) for the total entropy production.

What carries the argument

The invariance of Kubo's second fluctuation-dissipation theorem under the induced electric force, which preserves the Gaussian position probability density needed for the entropy production fluctuation theorem.

If this is right

  • The detailed fluctuation theorem is valid for the total entropy production.
  • For an Ornstein-Uhlenbeck friction kernel and oscillating electric field, specific expressions for averages hold.
  • Average work and entropy production depend on the parameters in analyzable regimes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This suggests similar invariance could occur for other external fields that couple uniformly to the bath.
  • Experimental realization with charged colloids under AC fields could test the Gaussian trajectories directly.
  • The result may generalize to other memory kernels beyond Ornstein-Uhlenbeck if the FDT structure is preserved.

Load-bearing premise

The electric field on the bath particles creates an induced force without altering Kubo's second fluctuation-dissipation theorem.

What would settle it

Numerical integration of the generalized Langevin equation with the induced force term, checking whether the position histogram remains Gaussian or shows deviations.

Figures

Figures reproduced from arXiv: 2605.03191 by J. I. Jim\'enez-Aquino, K. S. Rodr\'iguez-Vigil, M. A. Bastarrachea-Magnani.

Figure 1
Figure 1. Figure 1: FIG. 1. Average work and total entropy production in the Markovian and non-Markovian regimes in the overdamped limit. view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Average work and total entropy production in the Markovian and non-Markovian regimes in the underdamped limit. view at source ↗
read the original abstract

Fluctuation theorems are key to understanding both fundamental and applied aspects of non-equilibrium 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 (DFT) 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript studies the detailed fluctuation theorem (DFT) for total entropy production in a non-Markovian diffusion process of a charged particle confined in a harmonic potential and driven by a time-dependent electric field. Using a generalized Langevin equation (GLE) that includes an induced force arising from the field acting on both the tagged particle and the bath particles, the authors assert that Kubo's second fluctuation-dissipation theorem (FDT) remains exactly unchanged. This invariance is invoked to establish that the position process remains Gaussian along individual trajectories, which in turn allows a Crooks-type argument to prove the DFT. Explicit results are presented for an Ornstein-Uhlenbeck memory kernel and an oscillating electric field, together with numerical analysis of average work and entropy production in different parameter regimes.

Significance. If the claimed invariance of Kubo's FDT is placed on a firm microscopic footing, the work would usefully extend stochastic thermodynamics to non-Markovian systems in which external drives act on the bath as well as the system. Such situations arise in charged colloids, electrolytes, or dusty plasmas under AC fields, and the preservation of Gaussianity would allow standard fluctuation-theorem machinery to be applied without additional corrections. The concrete OU-kernel example and the accompanying parameter study provide testable predictions that could be checked in experiment or simulation.

major comments (1)
  1. [Derivation of the effective GLE after introduction of the induced force] The central claim that Kubo's second FDT remains unchanged (abstract and the paragraph introducing the effective GLE) is load-bearing for the entire DFT proof, because it supplies the noise correlator needed for Gaussianity of the position process. The manuscript asserts this invariance but does not supply the explicit projection calculation from the underlying microscopic dynamics that would demonstrate the absence of time-dependent corrections or multiplicative-noise terms induced by the uniform time-dependent field acting on the bath charges. Without that derivation, the subsequent steps that rely on an unmodified <ξ(t)ξ(s)> = kT K(t-s) cannot be verified.
minor comments (2)
  1. [Abstract] The abstract states that the FDT 'allows us to obtain the Gaussian probability density' but does not indicate whether this step is performed by direct solution of the linear SDE or by another route; a brief sentence clarifying the route would improve readability.
  2. [Equation defining the GLE] Notation for the memory kernel K(t) and the induced-force term should be introduced with a single consistent symbol set and cross-referenced to the GLE equation to avoid ambiguity when the entropy-production expression is written.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for recognizing the potential utility of our results in extending stochastic thermodynamics to non-Markovian systems driven by fields that act on the bath. We address the single major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: The central claim that Kubo's second FDT remains unchanged (abstract and the paragraph introducing the effective GLE) is load-bearing for the entire DFT proof, because it supplies the noise correlator needed for Gaussianity of the position process. The manuscript asserts this invariance but does not supply the explicit projection calculation from the underlying microscopic dynamics that would demonstrate the absence of time-dependent corrections or multiplicative-noise terms induced by the uniform time-dependent field acting on the bath charges. Without that derivation, the subsequent steps that rely on an unmodified <ξ(t)ξ(s)> = kT K(t-s) cannot be verified.

    Authors: We agree that an explicit microscopic derivation strengthens the central claim. In the revised manuscript we will add an appendix that performs the projection-operator calculation starting from the microscopic Hamiltonian of the tagged particle plus bath, with the uniform time-dependent electric field included for all charges. Because the field is spatially uniform, it shifts the equilibrium positions of the bath particles without altering their relative fluctuations or the linear response functions that define the memory kernel K(t). Consequently the random force ξ(t), which is generated by the initial bath conditions, retains the equilibrium correlator kT K(t-s) with no multiplicative or explicitly time-dependent corrections. The induced force appears only as a deterministic, additive term in the effective GLE. This establishes that the position process remains Gaussian for each realization, allowing the Crooks-type argument for the DFT to proceed unchanged. We believe the added derivation will fully address the referee's concern. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper adopts a generalized Langevin equation that includes an induced force from the time-dependent electric field acting on both tagged particle and bath. It explicitly claims to demonstrate that Kubo's second FDT remains unchanged under this setup, which then yields the Gaussian position PDF along trajectories and permits the standard Crooks-type argument for the detailed fluctuation theorem on total entropy production. Because the text states an explicit demonstration of FDT invariance (rather than treating it as an unexamined postulate or self-citation), the subsequent steps follow from that result without reducing to a definitional identity or fitted input. No self-citation load-bearing, ansatz smuggling, or renaming of known results is present; the derivation is self-contained against the chosen model and external benchmarks for fluctuation theorems.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the generalized Langevin equation for the charged particle, the invariance of Kubo's second FDT under the induced force, and the resulting Gaussian position statistics; no new entities are postulated.

free parameters (2)
  • Ornstein-Uhlenbeck memory kernel parameters
    Specific friction memory kernel chosen for the worked example; its parameters control the non-Markovian character.
  • oscillating electric field amplitude and frequency
    Time-dependent driving parameters used to analyze average work and entropy production in different regimes.
axioms (2)
  • domain assumption Kubo's second fluctuation-dissipation theorem remains unchanged when the electric field acts on both tagged particle and bath
    Invoked to obtain the Gaussian position PDF; stated as demonstrated but the abstract does not detail the steps.
  • domain assumption The position along a single stochastic trajectory follows a Gaussian probability density
    Direct consequence of the unchanged FDT; used as the key step for the DFT proof.

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    Calculation of⟨x(t)⟩ According to Eq. 33, we need theG(t)function for an OU-type friction memory kernel given by Eq. (73). In this case, the Laplace transform ofG(t)becomes ˆG(s) = s+a s3 +as 2 +bs+c ,(B1) wherea= 1/τ c,b=aγ 0 +k,c=ak. The denomina- tor is a third-degree polynomial, which has three roots following the conditions that the discriminant∆must...

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