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Entropy 2013, 15(11), 5065-5083; doi:10.3390/e15115065

Dynamics of Instantaneous Condensation in the ZRP Conditioned on an Atypical Current

1
School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, UK
2
Institut für Theoretische Physik, Universität zu Köln, Zülpicher Str. 77, Cologne 50937, Germany
3
Institute of Complex Systems II, Theoretical Soft Matter and Biophysics, Forschungszentrum Jülich, Jülich 52425, Germany
*
Author to whom correspondence should be addressed.
Received: 2 September 2013 / Revised: 30 October 2013 / Accepted: 5 November 2013 / Published: 19 November 2013
(This article belongs to the collection Advances in Applied Statistical Mechanics)
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Abstract

Using a generalized Doob’s h-transform we consider the zero-range process (ZRP) conditioned to carry an atypical current, with focus on the regime where the Gallavotti-Cohen symmetry loses its validity. For a single site we compute explicitly the boundary injection and absorption rates of an effective process which maps to a biased random walk. Our approach provides a direct probabilistic confirmation of the theory of “instantaneous condensation” which was proposed some while ago to explain the dynamical origin of the the failure of the Gallavotti-Cohen symmetry for high currents in the ZRP. However, it turns out that for stochastic dynamics with infinite state space care needs to be taken in the application of the Doob’s transform—we discuss in detail the sense in which the effective dynamics can be interpreted as “typical” for different regimes of the current phase diagram.
Keywords: zero-range process; Gallavotti-Cohen symmetry; large deviations; current fluctuations; condensation zero-range process; Gallavotti-Cohen symmetry; large deviations; current fluctuations; condensation
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Harris, R.J.; Popkov, V.; Schütz, G.M. Dynamics of Instantaneous Condensation in the ZRP Conditioned on an Atypical Current. Entropy 2013, 15, 5065-5083.

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