TY - JOUR

T1 - Void formation in diffusive lattice gases

AU - Krapivsky, P. L.

AU - Meerson, Baruch

AU - Sasorov, Pavel V.

PY - 2012/12

Y1 - 2012/12

N2 - What is the probability that a macroscopic void will spontaneously arise, at a specified time T, in an initially homogeneous gas? We address this question for diffusive lattice gases, and also determine the most probable density history leading to the void formation. We employ the macroscopic fluctuation theory by Bertini et al and consider both annealed and quenched averaging procedures (the initial condition is allowed to fluctuate in the annealed setting). We show that in the annealed case the void formation probability is given by the equilibrium Boltzmann-Gibbs formula, so the probability is independent of T (and also of the void shape, as only the volume matters). In the quenched case, which is intrinsically non-equilibrium, we evaluate the void formation probability analytically for non-interacting random walkers and probe it numerically for the simple symmetric exclusion process. For voids that are small compared with the diffusion length √ T, the equilibrium result for the void formation probability is recovered. We also re-derive our main results for non-interacting random walkers from an exact microscopic analysis.

AB - What is the probability that a macroscopic void will spontaneously arise, at a specified time T, in an initially homogeneous gas? We address this question for diffusive lattice gases, and also determine the most probable density history leading to the void formation. We employ the macroscopic fluctuation theory by Bertini et al and consider both annealed and quenched averaging procedures (the initial condition is allowed to fluctuate in the annealed setting). We show that in the annealed case the void formation probability is given by the equilibrium Boltzmann-Gibbs formula, so the probability is independent of T (and also of the void shape, as only the volume matters). In the quenched case, which is intrinsically non-equilibrium, we evaluate the void formation probability analytically for non-interacting random walkers and probe it numerically for the simple symmetric exclusion process. For voids that are small compared with the diffusion length √ T, the equilibrium result for the void formation probability is recovered. We also re-derive our main results for non-interacting random walkers from an exact microscopic analysis.

KW - diffusion

KW - exact results

KW - large deviations in non-equilibrium systems

KW - stochastic particle dynamics (theory)

UR - http://www.scopus.com/inward/record.url?scp=84871897522&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/2012/12/P12014

DO - 10.1088/1742-5468/2012/12/P12014

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AN - SCOPUS:84871897522

SN - 1742-5468

VL - 2012

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

IS - 12

M1 - P12014

ER -