2019/09/04 by Nir Gavish, Gavish, Nir, Pierre Nyquist +3 · 1 citation
Engineering · Materials Science · Physics and Astronomy · #35Q70 #37L05 #60F10 #60K35 #82C22 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Material Dynamics and Properties #Mathematical Physics (math-ph) #Phase Equilibria and Thermodynamics #Probability (math.PR) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1909.02054
openalex publication_date 2019/09/04 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
We study a system of hard rods of finite size in one space dimension, which\nmove by Brownian noise while avoiding overlap. We consider a scaling in which\nthe number of particles tends to infinity while the volume fraction of the rods\nremains constant; in this limit the empirical measure of the rod positions\nconverges almost surely to a deterministic limit evolution. We prove a\nlarge-deviation principle on path space for the empirical measure, by\nexploiting a one-to-one mapping between the hard-rod system and a system of\nnon-interacting particles on a shorter domain. The large-deviation principle\nnaturally identifies a gradient-flow structure for the limit evolution, with\nclear interpretations for both the driving functional (an `entropy') and the\ndissipation, which in this case is the Wasserstein dissipation.\n This study is inspired by recent developments in the continuum modelling of\nmultiple-species interacting particle systems with finite-size effects; for\nsuch systems many different modelling choices appear in the literature, raising\nthe question how one can understand such choices in terms of more microscopic\nmodels. The results of this paper give a clear answer to this question, albeit\nfor the simpler one-dimensional hard-rod system. For this specific system this\nresult provides a clear understanding of the value and interpretation of\ndifferent modelling choices, while giving hints for more general systems.\n