Large deviations and gradient flows for the Brownian one-dimensional hard-rod system
| Autor: | Nir Gavish, Mark A. Peletier, Pierre Nyquist |
|---|---|
| Přispěvatelé: | Applied Analysis, Center for Analysis, Scientific Computing & Appl., Mathematics and Computer Science, ICMS Affiliated, EAISI Foundational |
| Rok vydání: | 2019 |
| Předmět: |
math-ph
Steric interaction FOS: Physical sciences 35Q70 math.FA Continuum limit 01 natural sciences math.PR 37L05 Mathematics - Analysis of PDEs math.MP FOS: Mathematics Almost surely Limit (mathematics) Statistical physics 0101 mathematics Brownian motion Mathematical Physics math.AP Mathematics Particle system Entropy (statistical thermodynamics) 010102 general mathematics Probability (math.PR) Mathematical Physics (math-ph) 35Q70 60F10 82C22 60K35 37L05 Empirical measure Hard-rod Functional Analysis (math.FA) 010101 applied mathematics Mathematics - Functional Analysis Volume exclusion Large deviations 60K35 Brownian noise Large deviations theory Hard-sphere 82C22 Analysis Mathematics - Probability 60F10 Analysis of PDEs (math.AP) |
| Zdroj: | arXiv, 2019:1909.02054v1. Cornell University Library Potential Analysis, 58(1), 71-121. Springer |
| ISSN: | 0926-2601 |
| DOI: | 10.48550/arxiv.1909.02054 |
| Popis: | We study a system of hard rods of finite size in one space dimension, which move by Brownian noise while avoiding overlap. We consider a scaling in which the number of particles tends to infinity while the volume fraction of the rods remains constant; in this limit the empirical measure of the rod positions converges almost surely to a deterministic limit evolution. We prove a large-deviation principle on path space for the empirical measure, by exploiting a one-to-one mapping between the hard-rod system and a system of non-interacting particles on a shorter domain. The large-deviation principle naturally identifies a gradient-flow structure for the limit evolution, with clear interpretations for both the driving functional (an `entropy') and the dissipation, which in this case is the Wasserstein dissipation. This study is inspired by recent developments in the continuum modelling of multiple-species interacting particle systems with finite-size effects; for such systems many different modelling choices appear in the literature, raising the question how one can understand such choices in terms of more microscopic models. The results of this paper give a clear answer to this question, albeit for the simpler one-dimensional hard-rod system. For this specific system this result provides a clear understanding of the value and interpretation of different modelling choices, while giving hints for more general systems. Comment: Version 3 has an updated literature description |
| Databáze: | OpenAIRE |
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