Abstract
We consider hydrodynamic limits of interacting particles systems with open boundaries, where the exterior parameters change in a time scale slower than the typical relaxation time scale. The limit deterministic profiles evolve quasi-statically. These limits define rigorously the thermodynamic quasi static transformations also for transitions between non-equilibrium stationary states. We study first the case of the symmetric simple exclusion, where duality can be used, and then we use relative entropy methods to extend to other models like zero range systems. Finally we consider a chain of anharmonic oscillators in contact with a thermal Langevin bath with a temperature gradient and a slowly varying tension applied to one end.
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Acknowledgments
We thank Lorenzo Bertini, Claudio Landim, Giovanni Jona Lasinio and Errico Presutti for many very helpful discussions. We thank the kind hospitality of GSSI, AdM thanks also the Institute H. Poincare, where part of this work has been done. The work of S.O. has been partially supported by the European Advanced Grant Macroscopic Laws and Dynamical Systems (MALADY) (ERC AdG 246953).
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De Masi, A., Olla, S. Quasi-Static Hydrodynamic Limits. J Stat Phys 161, 1037–1058 (2015). https://doi.org/10.1007/s10955-015-1383-x
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DOI: https://doi.org/10.1007/s10955-015-1383-x