Non-reciprocally interacting Ornstein-Uhlenbeck processes: Exceptional points, Anomalous relaxation, Pseudo-equilibrium and Boundary refrigeration
Abstract
Non-reciprocal interactions are ubiquitous in active, biological, and disordered systems, generically driving them out of equilibrium. Here, we introduce a hierarchy of non-reciprocally interacting Ornstein-Uhlenbeck (NROU) models governed by a tunable non-reciprocity parameter g. At a special point g=g*, the drift matrix becomes non-diagonalizable, realizing exceptional points (EP's) of different orders, where eigenvalues and eigenvectors simultaneously coalesce. The hierarchy encompasses non-reciprocally coupled dimers, their disordered counterparts, and a many-body chain exactly mapping onto the paradigmatic Hatano-Nelson model in the arena of non-Hermitian quantum systems. For the disordered model, we show that the distribution of the EP location g* across disorder realizations develops a universal edge singularity precisely at the clean-system EP, and is manifestly non-self-averaging. Across all models, we find that at the EP, the usual exponential relaxation of the autocorrelation and covariance functions is dressed by a polynomial-in-time prefactor whose degree is set by the order of the EP and whose detailed structure encodes the spatial architecture of the chain. At complete asymmetry, the many-body chain exhibits ``pseudo-equilibrium'': its steady-state distribution factorizes into equilibrium-like single-particle measures despite a nonzero steady-state current. Moreover, the N-particle interacting system decomposes into N/2 independent complex OU processes. Finally, using the Harada-Sasa relation, we obtain a closed-form expression for the total steady-state heat dissipation and uncover a boundary refrigeration effect, in which the boundary particles switch from acting as a hot to a cold reservoir as the non-reciprocity is tuned.
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BibTeX
@misc{pal2026nonreciprocally,
title = {{Non-reciprocally interacting Ornstein-Uhlenbeck processes: Exceptional points, Anomalous relaxation, Pseudo-equilibrium and Boundary refrigeration}},
author = {Soumya Kanti Pal and Shamik Gupta},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05391},
eprint = {2609.05391},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05391},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Non-reciprocally interacting Ornstein-Uhlenbeck processes: Exceptional points, Anomalous relaxation, Pseudo-equilibrium and Boundary refrigeration
AU - Soumya Kanti Pal
AU - Shamik Gupta
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2609.05391
UR - https://arxiv.org/abs/2609.05391
AB - Non-reciprocal interactions are ubiquitous in active, biological, and disordered systems, generically driving them out of equilibrium. Here, we introduce a hierarchy of non-reciprocally interacting Ornstein-Uhlenbeck (NROU) models governed by a tunable non-reciprocity parameter g. At a special point g=g^*, the drift matrix becomes non-diagonalizable, realizing exceptional points (EP's) of different orders, where eigenvalues and eigenvectors simultaneously coalesce. The hierarchy encompasses non-reciprocally coupled dimers, their disordered counterparts, and a many-body chain exactly mapping onto the paradigmatic Hatano-Nelson model in the arena of non-Hermitian quantum systems. For the disordered model, we show that the distribution of the EP location g^* across disorder realizations develops a universal edge singularity precisely at the clean-system EP, and is manifestly non-self-averaging. Across all models, we find that at the EP, the usual exponential relaxation of the autocorrelation and covariance functions is dressed by a polynomial-in-time prefactor whose degree is set by the order of the EP and whose detailed structure encodes the spatial architecture of the chain. At complete asymmetry, the many-body chain exhibits ``pseudo-equilibrium'': its steady-state distribution factorizes into equilibrium-like single-particle measures despite a nonzero steady-state current. Moreover, the N-particle interacting system decomposes into N/2 independent complex OU processes. Finally, using the Harada-Sasa relation, we obtain a closed-form expression for the total steady-state heat dissipation and uncover a boundary refrigeration effect, in which the boundary particles switch from acting as a hot to a cold reservoir as the non-reciprocity is tuned.
ER -