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arxiv: 2512.03316 · v2 · submitted 2025-12-03 · ❄️ cond-mat.stat-mech · cond-mat.dis-nn

Symmetry Breaking of Current Response in Disordered Exclusion Processes

Issei Sakai , Takuma Akimoto This is my paper

Pith reviewed 2026-05-17 03:03 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.dis-nn
keywords disordered exclusion processesbias-reversal symmetrycurrent responsesymmetry breakingbond disordersite disordernonequilibrium transportasymmetric simple exclusion process
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The pith

The bias-reversal symmetry in disordered exclusion processes holds if and only if the local left-right bond-bias ratio is spatially uniform.

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

This paper establishes a general criterion for when bias-reversal symmetry holds in disordered exclusion processes. The symmetry means that reversing an external bias simply inverts the current magnitude without other changes, a property true in homogeneous systems like the asymmetric simple exclusion process. The authors demonstrate that the symmetry is preserved exactly when the ratio of left to right bond biases stays the same at every position in space. Mean-field theory and numerical checks show bond disorder leaves the symmetry intact even beyond linear response, while site disorder breaks it by coupling particle interactions to the heterogeneous environment. The result classifies different disordered setups and clarifies how disorder and interactions together shape nonequilibrium transport.

Core claim

In disordered exclusion processes the bias-reversal symmetry of the steady-state current holds if and only if the local left-right bond-bias ratio is spatially uniform. This criterion separates heterogeneous environments into symmetry-preserving and symmetry-breaking classes. Mean-field analysis and numerical simulations establish that bond disorder preserves the symmetry beyond linear response, whereas site disorder breaks it through the interplay between spatial heterogeneity and interparticle interactions.

What carries the argument

The spatial uniformity of the local left-right bond-bias ratio, which serves as the diagnostic separating symmetry-preserving bond disorder from symmetry-breaking site disorder.

If this is right

  • Bond disorder leaves bias-reversal symmetry intact even outside the linear-response regime.
  • Site disorder generates asymmetric current response by coupling heterogeneity to particle interactions.
  • The uniformity criterion supplies a practical diagnostic for classifying disordered environments.
  • Transport through biological and artificial nanochannels can exhibit symmetry breaking or preservation depending on the dominant disorder type.

Where Pith is reading between the lines

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

  • Engineered systems could use uniform bond biases to enforce symmetric transport even in the presence of other heterogeneity.
  • The same uniformity test might be applied to other driven diffusive models to predict when disorder breaks current symmetry.
  • Experiments that independently tune bond biases and site energies could directly map the boundary between the two disorder classes.

Load-bearing premise

Disorder effects can be cleanly separated into bond versus site types, and mean-field theory together with numerics fully capture how symmetry behaves beyond linear response.

What would settle it

A direct measurement or simulation showing that current magnitude changes upon bias reversal in a lattice where the left-right bond-bias ratio is identical at every site would falsify the claimed if-and-only-if criterion.

Figures

Figures reproduced from arXiv: 2512.03316 by Issei Sakai, Takuma Akimoto.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic illustration of the disordered ASEP. (a) [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Current-density relation in the ASEP with the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a)–(c): Symmetry indicators versus the bias magnit [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

The bias-reversal symmetry -- where reversing an external bias inverts the current without changing its magnitude -- is a hallmark of nonequilibrium transport. While this property holds in homogeneous systems such as the asymmetric simple exclusion process, how disorder and its interplay with particle interactions affect this symmetry has remained unclear. Here, we identify a general criterion in disordered exclusion processes showing that the bias-reversal symmetry holds if and only if the local left-right bond-bias ratio is spatially uniform. This criterion provides a practical diagnostic that separates heterogeneous environments into symmetry-preserving and symmetry-breaking classes. Mean-field and numerical analyses reveal that bond disorder preserves the symmetry beyond linear response, whereas site disorder breaks it through an interplay between heterogeneity and particle interactions. Our results demonstrate how environmental disorder and interparticle interactions cooperate to generate asymmetric transport, thereby providing insight that is potentially relevant to transport through biological and artificial nanochannels.

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 identifies a general criterion for bias-reversal symmetry (J(-F) = -J(F)) in disordered exclusion processes: the symmetry holds if and only if the local left-right bond-bias ratio r_i is spatially uniform. Bond disorder is shown to preserve the symmetry beyond linear response, while site disorder breaks it via the interplay between heterogeneity and hard-core interactions. The claim is supported by a mean-field closure of the steady-state master equation together with numerical simulations on finite chains.

Significance. If the central criterion is rigorously established, the work supplies a practical diagnostic that cleanly separates symmetry-preserving (bond-disorder) from symmetry-breaking (site-disorder) classes in nonequilibrium transport. This classification is potentially relevant to particle transport in biological and artificial nanochannels. The combination of mean-field analysis with direct numerics that extends beyond linear response constitutes a concrete strength.

major comments (1)
  1. [§3] §3 (mean-field closure of the current): The derivation of the 'only if' direction replaces joint occupation probabilities by products of single-site densities. In one-dimensional exclusion processes with site disorder, hard-core interactions generate persistent correlations that can produce an effective, position-dependent renormalization of the bias ratio even when the bare r_i is uniform. No error bound or comparison against exact small-system solutions is provided to control this approximation, which directly affects the necessity claim.
minor comments (2)
  1. [Figure 2] Figure 2 caption: the legend does not specify the disorder realization averaging procedure or the number of independent samples used for the error bars.
  2. [Eq. (3)] Notation: the definition of the local ratio r_i appears in two slightly different forms (Eq. (3) versus the text following Eq. (7)); a single, unambiguous expression would improve clarity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading, the positive assessment of the work's significance, and the constructive comment on the mean-field analysis. We address the concern point by point below and will revise the manuscript to strengthen the rigor of the necessity claim.

read point-by-point responses

  1. Referee: [§3] §3 (mean-field closure of the current): The derivation of the 'only if' direction replaces joint occupation probabilities by products of single-site densities. In one-dimensional exclusion processes with site disorder, hard-core interactions generate persistent correlations that can produce an effective, position-dependent renormalization of the bias ratio even when the bare r_i is uniform. No error bound or comparison against exact small-system solutions is provided to control this approximation, which directly affects the necessity claim.

    Authors: We agree that the mean-field closure neglects correlations generated by hard-core interactions, which in principle could renormalize the effective bias ratio in a position-dependent manner even for uniform bare r_i. Our numerical simulations solve the master equation directly on finite chains without invoking the mean-field closure and confirm that J(-F) = -J(F) holds if and only if the bare r_i is spatially uniform, for both bond and site disorder. To address the concern rigorously, the revised manuscript will include exact steady-state solutions for small lattices (N=3 to 6) obtained by direct diagonalization of the transition matrix, together with a quantitative comparison of the neglected correlation terms and an assessment of how they affect the symmetry condition. revision: yes

Circularity Check

0 steps flagged

No circularity: criterion derived from process structure, independent of inputs

full rationale

The paper derives the iff criterion for bias-reversal symmetry directly from the master equation structure of disordered exclusion processes, separating bond versus site disorder effects via explicit mean-field closure and numerical checks. No step reduces by construction to a fitted parameter, self-definition, or self-citation chain; the central claim is not equivalent to its inputs and remains falsifiable against external benchmarks such as exact solutions in homogeneous limits or direct simulations.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based on the abstract alone, the work relies on standard domain assumptions of exclusion processes but introduces no explicit free parameters or new entities; the criterion itself is the main addition.

axioms (1)
  • domain assumption The system is a one-dimensional Markovian exclusion process with either bond or site disorder.
    Invoked in the setup of the problem and the separation into symmetry-preserving and symmetry-breaking classes.

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Reference graph

Works this paper leans on

48 extracted references · 48 canonical work pages

  1. [1]

    Spitzer, Interaction of markov processes, Advances i n Mathematics 5, 246 (1970)

    F. Spitzer, Interaction of markov processes, Advances i n Mathematics 5, 246 (1970)

    work page 1970

  2. [2]

    Derrida, An exactly soluble non-equilibrium system: The asymmetric simple exclusion process, Physics Re- ports 301, 65 (1998)

    B. Derrida, An exactly soluble non-equilibrium system: The asymmetric simple exclusion process, Physics Re- ports 301, 65 (1998)

    work page 1998

  3. [3]

    B. Derrida, Non-equilibrium steady states: fluctuation s and large deviations of the density and of the current, Journal of Statistical Mechanics: Theory and Experi- ment 2007, P07023 (2007)

    work page 2007

  4. [4]

    De Masi and P

    A. De Masi and P. A. Ferrari, Self-diffusion in one- dimensional lattice gases in the presence of an external field, Journal of Statistical Physics 38, 603 (1985)

    work page 1985

  5. [5]

    Derrida and K

    B. Derrida and K. Mallick, Exact diffusion constant for the one-dimensional partially asymmetric exclusion model, Journal of Physics A: Mathematical and General 30, 1031 (1997)

    work page 1997

  6. [6]

    Berlioz, O

    T. Berlioz, O. B´ enichou, and A. Grabsch, Tracer and cur- rent fluctuations in driven diffusive systems, Phys. Rev. Lett. 134, 247101 (2025)

    work page 2025

  7. [7]

    Misakian and J

    M. Misakian and J. J. Kasianowicz, Electrostatic influ- ence on ion transport through the α hl channel, The Jour- nal of Membrane Biology 195, 137 (2003)

    work page 2003

  8. [8]

    E. M. Nestorovich, T. K. Rostovtseva, and S. M. Bezrukov, Residue ionization and ion transport through ompf channels, Biophysical Journal 85, 3718 (2003)

    work page 2003

  9. [9]

    S. Y. Noskov, W. Im, and B. Roux, Ion permeation through the α -hemolysin channel: Theoretical studies based on brownian dynamics and poisson-nernst-plank electrodiffusion theory, Biophysical Journal 87, 2299 (2004)

    work page 2004

  10. [10]

    Aksimentiev and K

    A. Aksimentiev and K. Schulten, Imaging α -hemolysin with molecular dynamics: Ionic conductance, osmotic permeability, and the electrostatic potential map, Bio- physical Journal 88, 3745 (2005)

    work page 2005

  11. [11]

    Y. Li, I. Berke, L. Chen, and Y. Jiang, Gating and inward rectifying properties of the mthk k+ channel with and without the gating ring, Journal of General Physiology 129, 109 (2007)

    work page 2007

  12. [12]

    Bhattacharya, J

    S. Bhattacharya, J. Muzard, L. Payet, J. Math´ e, U. Bock- elmann, A. Aksimentiev, and V. Viasnoff, Rectification of the current in α -hemolysin pore depends on the cation type: The alkali series probed by molecular dynamics simulations and experiments, The Journal of Physical Chemistry C 115, 4255 (2011)

    work page 2011

  13. [13]

    Piguet, F

    F. Piguet, F. Discala, M.-F. Breton, J. Pelta, L. Bacri, and A. Oukhaled, Electroosmosis through α -hemolysin that depends on alkali cation type, The Journal of Phys- ical Chemistry Letters 5, 4362 (2014)

    work page 2014

  14. [14]

    Payet, M

    L. Payet, M. Martinho, C. Merstorf, M. Pastoriza- Gallego, J. Pelta, V. Viasnoff, L. Auvray, M. Muthuku- mar, and J. Math´ e, Temperature effect on ionic cur- rent and ssdna transport through nanopores, Biophysical Journal 109, 1600 (2015)

    work page 2015

  15. [15]

    R. M. A. Manara, A. T. Guy, E. J. Wallace, and S. Khalid, Free-energy calculations reveal the subtle differences in the interactions of dna bases with α - hemolysin, Journal of Chemical Theory and Computa- tion 11, 810 (2015)

    work page 2015

  16. [16]

    S. A. Ionescu, S. Lee, N. G. Housden, R. Kaminska, C. Kleanthous, and H. Bayley, Orientation of the ompf porin in planar lipid bilayers, ChemBioChem 18, 554 (2017)

    work page 2017

  17. [17]

    W. Zhou, H. Qiu, Y. Guo, and W. Guo, Molecular in- sights into distinct detection properties of α -hemolysin, 6 mspa, csgg, and aerolysin nanopore sensors, The Journal of Physical Chemistry B 124, 1611 (2020)

    work page 2020

  18. [18]

    Dessaux, J

    D. Dessaux, J. Math´ e, R. Ramirez, and N. Basde- vant, Current rectification and ionic selectivity of α - hemolysin: Coarse-grained molecular dynamics simula- tions, The Journal of Physical Chemistry B 126, 4189 (2022)

    work page 2022

  19. [19]

    Donoghue, M

    A. Donoghue, M. Winterhalter, and T. Gutsmann, In- fluence of membrane asymmetry on ompf insertion, ori- entation and function, Membranes 13, 10.3390/mem- branes13050517 (2023)

    work page doi:10.3390/mem- 2023

  20. [20]

    Siwy, Ion-current rectification in nanopores and nan - otubes with broken symmetry, Advanced Functional Ma- terials 16, 735 (2006)

    Z. Siwy, Ion-current rectification in nanopores and nan - otubes with broken symmetry, Advanced Functional Ma- terials 16, 735 (2006)

    work page 2006

  21. [21]

    Y. Yan, L. Wang, J. Xue, and H.-C. Chang, Ion cur- rent rectification inversion in conic nanopores: Nonequi- librium ion transport biased by ion selectivity and spa- tial asymmetry, The Journal of Chemical Physics 138, 044706 (2013)

    work page 2013

  22. [22]

    Gamble, K

    T. Gamble, K. Decker, T. S. Plett, M. Pevarnik, J.-F. Pietschmann, I. Vlassiouk, A. Aksimentiev, and Z. S. Siwy, Rectification of ion current in nanopores depends on the type of monovalent cations: Experiments and modeling, The Journal of Physical Chemistry C 118, 9809 (2014)

    work page 2014

  23. [23]

    Su, W.-H

    Y.-S. Su, W.-H. Hung, A. R. Fauziah, Z. S. Siwy, and L.-H. Yeh, A ph gradient induced rectification inver- sion in asymmetric nanochannels leads to remarkably improved osmotic power, Chemical Engineering Journal 456, 141064 (2023)

    work page 2023

  24. [24]

    Tripathy and M

    G. Tripathy and M. Barma, Steady state and dynamics of driven diffusive systems with quenched disorder, Phys. Rev. Lett. 78, 3039 (1997)

    work page 1997

  25. [25]

    Tripathy and M

    G. Tripathy and M. Barma, Driven lattice gases with quenched disorder: Exact results and different macro- scopic regimes, Phys. Rev. E 58, 1911 (1998)

    work page 1911

  26. [26]

    Goldstein and E

    S. Goldstein and E. R. Speer, Reflection invariance of the current in the totally asymmetric simple exclusion process with disorder, Phys. Rev. E 58, 4226 (1998)

    work page 1998

  27. [27]

    Enaud and B

    C. Enaud and B. Derrida, Sample-dependent phase tran- sitions in disordered exclusion models, Europhysics Let- ters 66, 83 (2004)

    work page 2004

  28. [28]

    R. J. Harris and R. B. Stinchcombe, Disordered asym- metric simple exclusion process: Mean-field treatment, Phys. Rev. E 70, 016108 (2004)

    work page 2004

  29. [29]

    Juh´ asz, L

    R. Juh´ asz, L. Santen, and F. Igl´ oi, Partially asymmet - ric exclusion models with quenched disorder, Phys. Rev. Lett. 94, 010601 (2005)

    work page 2005

  30. [30]

    Juh´ asz, L

    R. Juh´ asz, L. Santen, and F. Igl´ oi, Partially asymmetric exclusion processes with sitewise disorder, Phys. Rev. E 74, 061101 (2006)

    work page 2006

  31. [31]

    Ebrahim Foulaadvand, S

    M. Ebrahim Foulaadvand, S. Chaaboki, and M. Saalehi, Characteristics of the asymmetric simple exclusion pro- cess in the presence of quenched spatial disorder, Phys. Rev. E 75, 011127 (2007)

    work page 2007

  32. [32]

    Greulich and A

    P. Greulich and A. Schadschneider, Single-bottleneck ap- proximation for driven lattice gases with disorder and open boundary conditions, Journal of Statistical Mechan- ics: Theory and Experiment 2008, P04009 (2008)

    work page 2008

  33. [33]

    M. E. Foulaadvand, A. B. Kolomeisky, and H. Teymouri, Asymmetric exclusion processes with disorder: Effect of correlations, Phys. Rev. E 78, 061116 (2008)

    work page 2008

  34. [34]

    R. J. Concannon and R. A. Blythe, Spatiotemporally complete condensation in a non-poissonian exclusion pro- cess, Phys. Rev. Lett. 112, 050603 (2014)

    work page 2014

  35. [35]

    Bahadoran and T

    C. Bahadoran and T. Bodineau, Properties and conjec- tures for the flux of TASEP with site disorder, Braz. J. Probab. Stat. 29, 282 (2015)

    work page 2015

  36. [36]

    Banerjee and A

    T. Banerjee and A. Basu, Smooth or shock: Universality in closed inhomogeneous driven single file motions, Phys. Rev. Res. 2, 013025 (2020)

    work page 2020

  37. [37]

    Haldar and A

    A. Haldar and A. Basu, Marching on a rugged land- scape: Universality in disordered asymmetric exclusion processes, Phys. Rev. Res. 2, 043073 (2020)

    work page 2020

  38. [38]

    Goswami, M

    A. Goswami, M. Chatterjee, and S. Mukherjee, Steady states and phase transitions in heterogeneous asymmet- ric exclusion processes, Journal of Statistical Mechanics : Theory and Experiment 2022, 123209 (2022)

    work page 2022

  39. [39]

    Sakai and T

    I. Sakai and T. Akimoto, Non-self-averaging of current in a totally asymmetric simple exclusion process with quenched disorder, Phys. Rev. E 107, L052103 (2023)

    work page 2023

  40. [40]

    Sakai and T

    I. Sakai and T. Akimoto, Sample-to-sample fluctuations of transport coefficients in the totally asymmetric simple exclusion process with quenched disorder, Phys. Rev. E 107, 054131 (2023)

    work page 2023

  41. [41]

    Supplemental Material for detailed derivations and ad di- tional numerical results

    work page

  42. [42]

    J. P. Bouchaud and A. Georges, Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications, Phys. Rep. 195 (1990)

    work page 1990

  43. [43]

    Hanney and M

    T. Hanney and M. R. Evans, Einstein relation for nonequilibrium steady states, Journal of Statistical Physics 111, 1377 (2003)

    work page 2003

  44. [44]

    Sakai and T

    I. Sakai and T. Akimoto, Unexpected effects of disorder on current fluctuations in the symmetric simple exclusion process, Phys. Rev. E 111, 014134 (2025)

    work page 2025

  45. [45]

    Akimoto and K

    T. Akimoto and K. Saito, Trace of anomalous diffusion in a biased quenched trap model, Phys. Rev. E 101, 042133 (2020)

    work page 2020

  46. [46]

    R. D. L. Hanes, C. Dalle-Ferrier, M. Schmiedeberg, M. C. Jenkins, and S. U. Egelhaaf, Colloids in one dimensional random energy landscapes, Soft Matter 8, 2714 (2012)

    work page 2012

  47. [47]

    S. Y. Yang, J.-A. Yang, E.-S. Kim, G. Jeon, E. J. Oh, K. Y. Choi, S. K. Hahn, and J. K. Kim, Single-file diffu- sion of protein drugs through cylindrical nanochannels, ACS Nano 4, 3817 (2010)

    work page 2010

  48. [48]

    M. Zhao, W. Wu, and B. Su, ph-controlled drug release by diffusion through silica nanochannel membranes, ACS Applied Materials & Interfaces 10, 33986 (2018). Supplemental Material for Symmetry Breaking of Current Response in Disordered Exclus ion Processes Issei Sakai 1, ∗ and Takuma Akimoto 1, † 1Department of Physics and Astronomy, Tokyo University of Sc...

    work page 2018