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Lower current large deviations for zero-range processes on a ring
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Chleboun, Paul, Grosskinsky, Stefan and Pizzoferrato, Andrea (2017) Lower current large deviations for zero-range processes on a ring. Journal of Statistical Physics, 167 (1). pp. 64-89. doi:10.1007/s10955-017-1740-z
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Official URL: http://dx.doi.org/10.1007/s10955-017-1740-z
Abstract
We study lower large deviations for the current of totally asymmetric zero-range processes on a ring with concave current-density relation. We use an approach by Jensen and Varadhan which has previously been applied to exclusion processes, to realize current fluctuations by travelling wave density profiles corresponding to non-entropic weak solutions of the hyperbolic scaling limit of the process. We further establish a dynamic transition, where large deviations of the current below a certain value are no longer typically attained by non-entropic weak solutions, but by condensed profiles, where a non-zero fraction of all the particles accumulates on a single fixed lattice site. This leads to a general characterization of the rate function, which is illustrated by providing detailed results for four generic examples of jump rates, including constant rates, decreasing rates, unbounded sublinear rates and asymptotically linear rates. Our results on the dynamic transition are supported by numerical simulations using a cloning algorithm.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science > Centre for Complexity Science Faculty of Science > Mathematics |
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| Library of Congress Subject Headings (LCSH): | Large deviations, Fluctuations (Physics), Condensation | ||||||||
| Journal or Publication Title: | Journal of Statistical Physics | ||||||||
| Publisher: | Springer New York LLC | ||||||||
| ISSN: | 0022-4715 | ||||||||
| Official Date: | April 2017 | ||||||||
| Dates: |
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| Volume: | 167 | ||||||||
| Number: | 1 | ||||||||
| Page Range: | pp. 64-89 | ||||||||
| DOI: | 10.1007/s10955-017-1740-z | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Open Access | ||||||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC), Gruppo nazionale di fisica matematica (Italy) | ||||||||
| Grant number: | EP/L505110/1 |
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