TY - JOUR

T1 - Macroscopic fluctuation theory of local time in lattice gases

AU - Smith, Naftali R.

AU - Meerson, Baruch

N1 - Publisher Copyright:
© 2024 Elsevier B.V.

PY - 2024/4/1

Y1 - 2024/4/1

N2 - The local time in an ensemble of particles measures the amount of time the particles spend in the vicinity of a given point in space. Here we study fluctuations of the empirical time average R=T−1∫0Tρx=0,tdt of the density ρx=0,t at the origin (so that R is the local time spent at the origin, rescaled by T) for an initially uniform one-dimensional diffusive lattice gas. We consider both the quenched and annealed initial conditions and employ the Macroscopic Fluctuation Theory (MFT). For a gas of non-interacting random walkers (RWs) the MFT yields exact large-deviation functions of R, which are closely related to the ones recently obtained by Burenev et al. (2023) using microscopic calculations for non-interacting Brownian particles. Our MFT calculations, however, additionally yield the most likely history of the gas density ρ(x,t) conditioned on a given value of R. Furthermore, we calculate the variance of the local time fluctuations for arbitrary particle- or energy-conserving diffusive lattice gases. Better known examples of such systems include the simple symmetric exclusion process, the Kipnis-Marchioro-Presutti model and the symmetric zero-range process. Our results for the non-interacting RWs can be readily extended to a step-like initial condition for the density.

AB - The local time in an ensemble of particles measures the amount of time the particles spend in the vicinity of a given point in space. Here we study fluctuations of the empirical time average R=T−1∫0Tρx=0,tdt of the density ρx=0,t at the origin (so that R is the local time spent at the origin, rescaled by T) for an initially uniform one-dimensional diffusive lattice gas. We consider both the quenched and annealed initial conditions and employ the Macroscopic Fluctuation Theory (MFT). For a gas of non-interacting random walkers (RWs) the MFT yields exact large-deviation functions of R, which are closely related to the ones recently obtained by Burenev et al. (2023) using microscopic calculations for non-interacting Brownian particles. Our MFT calculations, however, additionally yield the most likely history of the gas density ρ(x,t) conditioned on a given value of R. Furthermore, we calculate the variance of the local time fluctuations for arbitrary particle- or energy-conserving diffusive lattice gases. Better known examples of such systems include the simple symmetric exclusion process, the Kipnis-Marchioro-Presutti model and the symmetric zero-range process. Our results for the non-interacting RWs can be readily extended to a step-like initial condition for the density.

KW - Large deviation theory

KW - Lattice gases

KW - Macroscopic fluctuation theory

KW - Stochastic processes

UR - http://www.scopus.com/inward/record.url?scp=85187692755&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2024.129616

DO - 10.1016/j.physa.2024.129616

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AN - SCOPUS:85187692755

SN - 0378-4371

VL - 639

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

M1 - 129616

ER -