Hydrodynamical behavior for the symmetric simple partial exclusion with open boundary

DOI10.1007/S11040-023-09446-9zbMATH Open1515.60266arXiv2201.10241OpenAlexW4375864143MaRDI QIDQ6155596

No author found.

Publication date: 5 June 2023

Published in: Mathematical Physics, Analysis and Geometry (Search for Journal in Brave)

Abstract: We analyze the generalized symmetric exclusion process, which allows at most $alpha$ particles per site, and we put it in contact with stochastic reservoirs whose strength is regulated by a parameter $hetainmathbbR$. We prove that the hydrodynamic behavior is given by the heat equation and depending on the value of $heta$, the equation is supplemented with different boundary conditions. Setting $alpha=1$ we find the results known in [1] for the symmetric simple exclusion process.

Full work available at URL: https://arxiv.org/abs/2201.10241

zbMATH Keywords

heat equationhydrodynamic limitpartial exclusion process

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Heat equation (35K05) Continuous-time Markov processes on discrete state spaces (60J27)

Cites Work

• Unnamed Item
• Duality for stochastic models of transport
• Nonlinear diffusion limit for a system with nearest neighbor interactions
• Interaction of Markov processes
• Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations
• Symmetric inclusion process with slow boundary: hydrodynamics and hydrostatics
• Non-equilibrium and stationary fluctuations for the SSEP with slow boundary
• Hydrodynamics of porous medium model with slow reservoirs
• Hydrodynamics for the partial exclusion process in random environment
• Exclusion process with slow boundary
• Exact formulas for two interacting particles and applications in particle systems with duality
• Hydrodynamic Limit for a Nongradient Interacting Particle System with Stochastic Reservoirs
• Exact solution of a 1D asymmetric exclusion model using a matrix formulation
• Higher order hydrodynamics and equilibrium fluctuations of interacting particle systems
• Hydrostatic limit for exclusion process with slow boundary revisited
• Slow to fast infinitely extended reservoirs for the symmetric exclusion process with long jumps

Related Items (5)

Unnamed Item ⋮ On a class of solvable stationary non equilibrium states for mass exchange models ⋮ Current fluctuations in a semi-infinite line ⋮ Density fluctuations for the multi-species stirring process ⋮ Large deviations in the symmetric simple exclusion process with slow boundaries: a hydrodynamic perspective

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