PreprintarXiv licencearXiv
Loss of memory in the periodic Ehrenfest model with small polyhedral scatterers
Abstract
We determine the Boltzmann--Grad limit of the Ehrenfest ``wind-tree'' model with a periodic configuration of polyhedral scatterers. The central result is a loss-of-memory effect in dimension d≥ 3 for a generic choice of polyhedron. This yields a Markovian limiting transport process on an extended state space and a generalised linear Boltzmann equation for the time evolution of the particle density.
Related
- Polyhedral Methods for Cooperative Games: Small Lifts and Hard Faces
- Rotating-Memory Fibonacci Numbers and Periodic Tilings
- Schrödinger estimates with arbitrarily small periodic regularity on ℍ2 × 𝕋
- A Generalized Source Integral Equation for Homogeneous Penetrable Scatterers
- Boundary Control of a Modified Timoshenko-Ehrenfest Beam via Reduced-Order Reinforcement Learning
BibTeX
@misc{lutsko2026loss,
title = {{Loss of memory in the periodic Ehrenfest model with small polyhedral scatterers}},
author = {Christopher Lutsko and Jens Marklof},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04371},
eprint = {2609.04371},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04371},
}
RIS
TY - UNPB
TI - Loss of memory in the periodic Ehrenfest model with small polyhedral scatterers
AU - Christopher Lutsko
AU - Jens Marklof
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.04371
UR - https://arxiv.org/abs/2609.04371
AB - We determine the Boltzmann--Grad limit of the Ehrenfest ``wind-tree'' model with a periodic configuration of polyhedral scatterers. The central result is a loss-of-memory effect in dimension d≥ 3 for a generic choice of polyhedron. This yields a Markovian limiting transport process on an extended state space and a generalised linear Boltzmann equation for the time evolution of the particle density.
ER -