A Variational Structure for Interacting Particle Systems and their Hydrodynamic Scaling Limits

Marcus Kaiser; Robert L. Jack; Johannes Zimmer

doi:10.4310/CMS.2019.v17.n3.a7

A Variational Structure for Interacting Particle Systems and their Hydrodynamic Scaling Limits

Marcus Kaiser, Robert L. Jack, Johannes Zimmer

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Abstract

We consider hydrodynamic scaling limits for a class of reversible interacting particle systems, which includes the symmetric simple exclusion process and certain zero-range processes. We study a (non-quadratic) microscopic action functional for these systems. We analyse the behaviour of this functional in the hydrodynamic limit and we establish conditions under which it converges to the (quadratic) action functional of Macroscopic Fluctuation Theory. We discuss the implications of these results for rigorous analysis of hydrodynamic limits.

Original language	English
Pages (from-to)	739-780
Number of pages	42
Journal	Communications in Mathematical Sciences
Volume	17
Issue number	3
DOIs	https://doi.org/10.4310/CMS.2019.v17.n3.a7
Publication status	Published - 30 Aug 2019

Keywords

math-ph
math.AP
math.MP

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10.4310/CMS.2019.v17.n3.a7

scaling_limits-rev.PDF
© 2019 M. Kaiser, R. L. Jack and J. Zimmer. The final publication is available at Communications in Mathematical Sciences via https://doi.org/10.4310/CMS.2019.v17.n3.a7
Accepted author manuscript, 343 KB

Cite this

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abstract = " We consider hydrodynamic scaling limits for a class of reversible interacting particle systems, which includes the symmetric simple exclusion process and certain zero-range processes. We study a (non-quadratic) microscopic action functional for these systems. We analyse the behaviour of this functional in the hydrodynamic limit and we establish conditions under which it converges to the (quadratic) action functional of Macroscopic Fluctuation Theory. We discuss the implications of these results for rigorous analysis of hydrodynamic limits. ",

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AB - We consider hydrodynamic scaling limits for a class of reversible interacting particle systems, which includes the symmetric simple exclusion process and certain zero-range processes. We study a (non-quadratic) microscopic action functional for these systems. We analyse the behaviour of this functional in the hydrodynamic limit and we establish conditions under which it converges to the (quadratic) action functional of Macroscopic Fluctuation Theory. We discuss the implications of these results for rigorous analysis of hydrodynamic limits.

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A Variational Structure for Interacting Particle Systems and their Hydrodynamic Scaling Limits

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Analysis of the Effective Long Time-Behaviour of Molecule Systems

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A Variational Structure for Interacting Particle Systems and their Hydrodynamic Scaling Limits

Abstract

Keywords

Access to Document

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Fingerprint

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Analysis of the Effective Long Time-Behaviour of Molecule Systems

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