Current fluctuations in the symmetric zero-range process below and at critical density
arXiv:2406.01346 · doi:10.1103/PhysRevE.110.L052103
Abstract
Characterizing current fluctuations in a steady state is of fundamental interest and has attracted considerable attention in the recent past. However, the bulk of the studies are limited to systems that either do not exhibit a phase transition or are far from criticality. Here we consider a symmetric zero-range process on a ring that is known to show a phase transition in the steady state. We analytically calculate two density-dependent transport coefficients, namely, the bulk-diffusion coefficient and the particle mobility, that characterize the first two cumulants of the time-integrated current. We show that on the hydrodynamic scale, away from the critical point, the variance of the time-integrated current in the steady state grows with time as and at short and long times, respectively. Moreover, we find an expression of the full scaling function for the variance of the time-integrated current and thereby the amplitude of the temporal growth of the current fluctuations. At the critical point, using a scaling theory, we find that, while the above-mentioned long-time scaling of the variance of the cumulative current continues to hold, the short-time behavior is anomalous in that the growth exponent is larger than one-half and varies continuously with the model parameters.
5 pages, 2 figures + 5 supplemental pages (2 supplemental figures)
References in corpus (30)
- Non equilibrium steady states: fluctuations and large deviations of the density and of the current
- Macroscopic fluctuation theory
- Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
- Macroscopic fluctuation theory for stationary non equilibrium states
- Current fluctuations in non-equilibrium diffusive systems: an additivity principle
- Fluctuations in Stationary non Equilibrium States
- A pedestrian's view on interacting particle systems, KPZ universality, and random matrices
- A momentum conserving model with anomalous thermal conductivity in low dimension
- Universal cumulants of the current in diffusive systems on a ring
- Large Deviations in Single File Diffusion
- Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition
- Canonical Analysis of Condensation in Factorised Steady State
- Current fluctuations in the zero-range process with open boundaries
- Fluctuations of Current in Non-Stationary Diffusive Lattice Gases
- Theory of Single File Diffusion in a Force Field
- DMRG-study of current and activity fluctuations near non-equilibrium phase transitions
- Current fluctuations in non-interacting run-and-tumble particles in one-dimension
- Current Fluctuations and Statistics During a Large Deviation Event in an Exactly-Solvable Transport Model
- Current fluctuations of interacting active Brownian particles
- Equilibrium-like fluctuations in some boundary-driven open diffusive systems
- Flux fluctuations in the one dimensional nearest neighbors symmetric simple exclusion process
- Correlations of the density and of the current in non-equilibrium diffusive systems
- Locating the minimum : Approach to equilibrium in a disordered, symmetric zero range process
- Current fluctuations in nonequilibrium discontinuous phase transitions
- Current fluctuations at a phase transition
- Current fluctuations in an interacting active lattice gas
- Dynamic correlations in the conserved Manna sandpile
- Anomalous relaxation and hyperuniform fluctuations in center-of-mass conserving systems with broken time-reversal symmetry
- Time-dependent properties of run-and-tumble particles. II.: Current fluctuations
- Two-point correlation function of an exclusion process with hole-dependent rates