Quasi-static limit for the asymmetric simple exclusion

• 成果类型: Article
• 署名作者: De Masi, Anna; Marchesani, Stefano; Olla, Stefano; Xu, Lu
• 署名单位: University of L'Aquila; Gran Sasso Science Institute (GSSI); Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Institut Universitaire de France
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-022-01140-1
• 发表日期: 2022
• 页码: 1075-1117
• 关键词: hydrodynamic limit

摘要

We study the one-dimensional asymmetric simple exclusion process on the lattice (1, ..., N) with creation/annihilation at the boundaries. The boundary rates are time dependent and change on a slow time scale N-a with a > 0. We prove that at the time scale N1+a the system evolves quasi-statically with a macroscopic density profile given by the entropy solution of the stationary Burgers equation with boundary densities changing in time, determined by the corresponding microscopic boundary rates. We consider two different types of boundary rates: the Liggett boundaries that correspond to the projection of the infinite dynamics, and the reversible boundaries, that correspond to the contact with particle reservoirs in equilibrium. The proof is based on the control of the Lax boundary entropy-entropy flux pairs and a coupling argument.