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Asymptotics of work distributions in a stochastically driven system
Stockholm University, Faculty of Science, Department of Physics.
Stockholm University, Faculty of Science, Department of Physics.
Number of Authors: 22017 (English)In: European Physical Journal B: Condensed Matter Physics, ISSN 1434-6028, E-ISSN 1434-6036, Vol. 90, no 12, article id 258Article in journal (Refereed) Published
Abstract [en]

We determine the asymptotic forms of work distributions at arbitrary times T, in a class of driven stochastic systems using a theory developed by Nickelsen and Engel (EN theory) [D. Nickelsen and A. Engel, Eur. Phys. J. B 82 , 207 (2011)], which is based on the contraction principle of large deviation theory. In this paper, we extend the theory, previously applied in the context of deterministically driven systems, to a model in which the driving is stochastic. The models we study are described by overdamped Langevin equations and the work distributions in path integral form, are characterised by having quadratic augmented actions. We first illustrate EN theory, for a deterministically driven system - the breathing parabola model, and show that within its framework, the Crooks fluctuation theorem manifests itself as a reflection symmetry property of a certain characteristic polynomial, which also determines the exact moment-generating-function at arbitrary times. We then extend our analysis to a stochastically driven system, studied in references [S. Sabhapandit, EPL 89 , 60003 (2010); A. Pal, S. Sabhapandit, Phys. Rev. E 87 , 022138 (2013); G. Verley, C. Van den Broeck, M. Esposito, New J. Phys. 16 , 095001 (2014)], for both equilibrium and non-equilibrium steady state initial distributions. In both cases we obtain new analytic solutions for the asymptotic forms of (dissipated) work distributions at arbitrary T. For dissipated work in the steady state, we compare the large T asymptotic behaviour of our solution to the functional form obtained in reference [New J. Phys. 16 , 095001 (2014)]. In all cases, special emphasis is placed on the computation of the pre-exponential factor and the results show excellent agreement with numerical simulations. Our solutions are exact in the low noise (beta -> (infinity)) limit.

Place, publisher, year, edition, pages
2017. Vol. 90, no 12, article id 258
Keywords [en]
Statistical and Nonlinear Physics
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:su:diva-150952DOI: 10.1140/epjb/e2017-80432-9ISI: 000418431900002OAI: oai:DiVA.org:su-150952DiVA, id: diva2:1174084
Available from: 2018-01-15 Created: 2018-01-15 Last updated: 2018-01-15Bibliographically approved

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Manikandan, Sreekanth K.Krishnamurthy, Supriya
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