Non-equilibrium density fluctuations for the stirring process with weak boundary dynamics
Abstract
We consider the one-dimensional stirring process on the segment {−N,…,N}, coupled to boundary dynamics that inject particles from the right reservoir and remove particles from the left reservoir, each acting on a window of size K. We investigate the non-equilibrium fluctuations of the system, starting from a product measure associated with a smooth initial profile. The limit Ornstein-Uhlenbeck process is given in terms of the Laplacian and gradient operators acting on test functions satisfying time-dependent Robin boundary conditions that are obtained by linearizing the boundary conditions in the hydrodynamic equation. A central ingredient in our analysis is the derivation of sharp bounds on the space and space-time v-functions of arbitrary degree for the centered occupation variables; these bounds were proved in the companion article \cite{birmpa2025nonequilibriumfluctuationsstirringprocess}.
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BibTeX
@misc{birmpa2026nonequilibrium,
title = {{Non-equilibrium density fluctuations for the stirring process with weak boundary dynamics}},
author = {Panagiota Birmpa and Patrícia Gonçalves and Dimitrios Tsagkarogiannis},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32701},
eprint = {2610.32701},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32701},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Non-equilibrium density fluctuations for the stirring process with weak boundary dynamics
AU - Panagiota Birmpa
AU - Patrícia Gonçalves
AU - Dimitrios Tsagkarogiannis
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32701
UR - https://arxiv.org/abs/2610.32701
AB - We consider the one-dimensional stirring process on the segment {−N,…,N}, coupled to boundary dynamics that inject particles from the right reservoir and remove particles from the left reservoir, each acting on a window of size K. We investigate the non-equilibrium fluctuations of the system, starting from a product measure associated with a smooth initial profile. The limit Ornstein-Uhlenbeck process is given in terms of the Laplacian and gradient operators acting on test functions satisfying time-dependent Robin boundary conditions that are obtained by linearizing the boundary conditions in the hydrodynamic equation. A central ingredient in our analysis is the derivation of sharp bounds on the space and space-time v-functions of arbitrary degree for the centered occupation variables; these bounds were proved in the companion article \cite{birmpa2025nonequilibriumfluctuationsstirringprocess}.
ER -