Sample-specific rectification-like response in a boundary-driven exclusion process
Abstract
We investigate the current response of a boundary-driven symmetric exclusion process with quenched site disorder. Hard-core particles hop symmetrically on a one-dimensional lattice with site-dependent rates and are injected and removed at the boundaries by two reservoirs of different densities. We approximate the steady-state density profile using a Galerkin projection at linear order and a mean-field closure at higher orders, and thereby obtain the current as a nonlinear function of the reservoir density difference. At linear order in the reservoir density difference, the current-response coefficient depends on the mean reservoir density ρ, in contrast to the homogeneous case. Through the linear-response relation, this dependence leads to an equilibrium current-fluctuation coefficient that is asymmetric under ρ→ 1−ρ. Beyond linear response, nonzero even-order current contributions break the antisymmetry of the current under reversal of the reservoir density difference, producing rectification-like behavior in individual disorder realizations. We further show that spatial-reflection symmetry of the equilibrium density profile rules out such behavior, so broken spatial-reflection symmetry of the profile is a necessary condition for rectification-like behavior. Within the present approximation, we further find that, for continuously distributed site disorder, rectification-like behavior occurs arbitrarily close to equilibrium for almost every disorder realization. At the ensemble level, however, the disorder-averaged current remains antisymmetric because the disorder ensemble is invariant under spatial reflection. These results provide a mechanism for rectification-like transport arising from sample-specific spatial heterogeneity rather than from an explicitly imposed directional asymmetry.
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BibTeX
@misc{sakai2026samplespecific,
title = {{Sample-specific rectification-like response in a boundary-driven exclusion process}},
author = {Issei Sakai and Takuma Akimoto},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03560},
eprint = {2609.03560},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03560},
}
RIS
TY - UNPB
TI - Sample-specific rectification-like response in a boundary-driven exclusion process
AU - Issei Sakai
AU - Takuma Akimoto
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03560
UR - https://arxiv.org/abs/2609.03560
AB - We investigate the current response of a boundary-driven symmetric exclusion process with quenched site disorder. Hard-core particles hop symmetrically on a one-dimensional lattice with site-dependent rates and are injected and removed at the boundaries by two reservoirs of different densities. We approximate the steady-state density profile using a Galerkin projection at linear order and a mean-field closure at higher orders, and thereby obtain the current as a nonlinear function of the reservoir density difference. At linear order in the reservoir density difference, the current-response coefficient depends on the mean reservoir density ρ, in contrast to the homogeneous case. Through the linear-response relation, this dependence leads to an equilibrium current-fluctuation coefficient that is asymmetric under ρ→ 1−ρ. Beyond linear response, nonzero even-order current contributions break the antisymmetry of the current under reversal of the reservoir density difference, producing rectification-like behavior in individual disorder realizations. We further show that spatial-reflection symmetry of the equilibrium density profile rules out such behavior, so broken spatial-reflection symmetry of the profile is a necessary condition for rectification-like behavior. Within the present approximation, we further find that, for continuously distributed site disorder, rectification-like behavior occurs arbitrarily close to equilibrium for almost every disorder realization. At the ensemble level, however, the disorder-averaged current remains antisymmetric because the disorder ensemble is invariant under spatial reflection. These results provide a mechanism for rectification-like transport arising from sample-specific spatial heterogeneity rather than from an explicitly imposed directional asymmetry.
ER -