Journal of Statistical Physics

, Volume 175, Issue 2, pp 402–417 | Cite as

Particle Model for the Reservoirs in the Simple Symmetric Exclusion Process

  • Thu Dang Thien NguyenEmail author


In this paper, we will study the long time behavior of the simple symmetric exclusion process in the “channel” \(\varLambda _N=[1,N]\cap \mathbb {N}\) with reservoirs at the boundaries. These reservoirs are also systems of particles which can be exchanged with the particles in the channel. The size M of each reservoir is much larger than the one of the channel, i.e. \(M=N^{1+\alpha }\) for a fixed number \(\alpha >0\). Based on the size of the channel and the holding time at each reservoir, we will investigate some types of rescaling time.


Hydrodynamic limits Adiabatic limits Ideal reservoir limits Global equilibrium limits 



I am truly grateful to Prof. Errico Presutti for providing me with so many worthwhile suggestions and helpful advices throughout discussion sessions.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Gran Sasso Science InstituteL’AquilaItaly
  2. 2.Department of MathematicsUniversity of QuynhonQuy NhonVietnam

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