Exact Microscopic One-Body Reduction in the Symmetric Exclusion Process
Abstract
The symmetric exclusion process (SEP) is a paradigmatic model of interacting particle transport. Its current--density correlations are governed by an infinite many-body hierarchy of equations. Only recently, this hierarchy was found to collapse at large scales onto a single closed equation. Is this remarkable simplification created by coarse graining, or does it reflect a deeper property already present in the microscopic dynamics? Here we show that the second scenario is realized. At arbitrary time on the lattice, the entire hierarchy collapses onto a single linear equation which is exactly equivalent to a persistence problem for a single auxiliary random walker. Thus an interacting many-body problem reduces exactly to a genuine one-body problem before any scaling limit is taken. This reduction determines the complete finite-time correlation profile, including during nonequilibrium relaxation. More broadly, the microscopic operator uncovered here opens a route to more general correlation functions in the SEP, and may point to a general organizing principle for nonequilibrium interacting particle systems.
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BibTeX
@misc{benichou2026exact,
title = {{Exact Microscopic One-Body Reduction in the Symmetric Exclusion Process}},
author = {Olivier Bénichou and Aurélien Grabsch},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18626},
eprint = {2610.18626},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18626},
}
RIS
TY - UNPB
TI - Exact Microscopic One-Body Reduction in the Symmetric Exclusion Process
AU - Olivier Bénichou
AU - Aurélien Grabsch
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18626
UR - https://arxiv.org/abs/2610.18626
AB - The symmetric exclusion process (SEP) is a paradigmatic model of interacting particle transport. Its current--density correlations are governed by an infinite many-body hierarchy of equations. Only recently, this hierarchy was found to collapse at large scales onto a single closed equation. Is this remarkable simplification created by coarse graining, or does it reflect a deeper property already present in the microscopic dynamics? Here we show that the second scenario is realized. At arbitrary time on the lattice, the entire hierarchy collapses onto a single linear equation which is exactly equivalent to a persistence problem for a single auxiliary random walker. Thus an interacting many-body problem reduces exactly to a genuine one-body problem before any scaling limit is taken. This reduction determines the complete finite-time correlation profile, including during nonequilibrium relaxation. More broadly, the microscopic operator uncovered here opens a route to more general correlation functions in the SEP, and may point to a general organizing principle for nonequilibrium interacting particle systems.
ER -