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PreprintCC BY-NC-ND 4.0HAL

Dynamical and stationary non-equilibrium fluctuations for a boundary-driven exclusion process with energy

  • Hugo da Cunha
Open at sourcePDFDOICite

Abstract

We consider the exclusion process with energy, a model with mass and energy conservation, and we put it in a boundary-driven setting. We are interested in its hydrodynamic and hydrostatic limits, together with the associated dynamical and stationary fluctuations. We provide a new proof for the derivation of dynamical fluctuations that does not require explicit estimates on the two-point correlation functions. While the hydrodynamic limit is given by two uncoupled heat equations, the dynamical fluctuations are described by a system of coupled generalized Ornstein-Uhlenbeck processes.

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Cite

BibTeXRIS
BibTeX
@misc{cunha2026dynamical,
  title = {{Dynamical and stationary non-equilibrium fluctuations for a boundary-driven exclusion process with energy}},
  author = {Hugo da Cunha},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08701},
  eprint = {2609.08701},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05743306v1},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Dynamical and stationary non-equilibrium fluctuations for a boundary-driven exclusion process with energy
AU  - Hugo da Cunha
PY  - 2026
DA  - 2026/09/08
PB  - HAL
DO  - 10.48550/arxiv.2609.08701
UR  - https://hal.science/hal-05743306v1
AB  - We consider the exclusion process with energy, a model with mass and energy conservation, and we put it in a boundary-driven setting. We are interested in its hydrodynamic and hydrostatic limits, together with the associated dynamical and stationary fluctuations. We provide a new proof for the derivation of dynamical fluctuations that does not require explicit estimates on the two-point correlation functions. While the hydrodynamic limit is given by two uncoupled heat equations, the dynamical fluctuations are described by a system of coupled generalized Ornstein-Uhlenbeck processes.
ER  -