TY - JOUR

T1 - Extreme fluctuations of current in the symmetric simple exclusion process

T2 - A non-stationary setting

AU - Vilenkin, A.

AU - Meerson, B.

AU - Sasorov, P. V.

PY - 2014/6/1

Y1 - 2014/6/1

N2 - We use the macroscopic fluctuation theory (MFT) to evaluate the probability distribution P of extreme values of integrated current J at a specified time t = T in the symmetric simple exclusion process (SSEP) on an infinite line. As shown recently (Meerson and Sasorov 2014 Phys. Rev. E 89 010101), the SSEP belongs to the elliptic universality class. Here, for very large currents, the diffusion terms of the MFT equations can be neglected compared with the terms coming from the shot noise. Using the hodograph transformation and an additional change of variables, we reduce the 'inviscid' MFT equations to Laplace's equation in an extended space. This opens the way to an exact solution. Here we solve the extreme-current problem for a flat deterministic initial density profile with an arbitrary density 0 < n0 < 1. The solution yields the most probable density history of the system conditional on the extreme current, J / √T →∞ and leads to a super-Gaussian extreme-current statistics, ln -rfpag≃-(n0)J3 /T , in agreement with Derrida and Gerschenfeld (2009 J. Stat. Phys. 137 978). We calculate the function φ(n0) analytically. It is symmetric with respect to the half-filling density n0 = 1/2, diverges at n0 → 0 and n0 → 1 and exhibits a singularity φ(n0) |n 0-1/2| at the half-filling density n0 = 1/2.

AB - We use the macroscopic fluctuation theory (MFT) to evaluate the probability distribution P of extreme values of integrated current J at a specified time t = T in the symmetric simple exclusion process (SSEP) on an infinite line. As shown recently (Meerson and Sasorov 2014 Phys. Rev. E 89 010101), the SSEP belongs to the elliptic universality class. Here, for very large currents, the diffusion terms of the MFT equations can be neglected compared with the terms coming from the shot noise. Using the hodograph transformation and an additional change of variables, we reduce the 'inviscid' MFT equations to Laplace's equation in an extended space. This opens the way to an exact solution. Here we solve the extreme-current problem for a flat deterministic initial density profile with an arbitrary density 0 < n0 < 1. The solution yields the most probable density history of the system conditional on the extreme current, J / √T →∞ and leads to a super-Gaussian extreme-current statistics, ln -rfpag≃-(n0)J3 /T , in agreement with Derrida and Gerschenfeld (2009 J. Stat. Phys. 137 978). We calculate the function φ(n0) analytically. It is symmetric with respect to the half-filling density n0 = 1/2, diverges at n0 → 0 and n0 → 1 and exhibits a singularity φ(n0) |n 0-1/2| at the half-filling density n0 = 1/2.

KW - current fluctuations

KW - diffusion

KW - large deviations in non-equilibrium systems

KW - stochastic particle dynamics (theory)

UR - http://www.scopus.com/inward/record.url?scp=84903639602&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/2014/06/P06007

DO - 10.1088/1742-5468/2014/06/P06007

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AN - SCOPUS:84903639602

SN - 1742-5468

VL - 2014

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

IS - 6

M1 - P06007

ER -