Role of initial conditions in $1D$ diffusive systems: compressibility, hyperuniformity and long-term memory

Abstract

We analyse the long-lasting effects of initial conditions on fluctuations in one-dimensional diffusive systems. We consider both the fluctuations of current for non-interacting diffusive particles starting from a step-like initial density profile, and the mean-square displacement of tracers in homogeneous systems with single-file diffusion. For these two cases, we show analytically (via the propagator and Macroscopic Fluctuation Theory, respectively) that the long-term memory of initial conditions is mediated by a single static quantity: a generalized compressibility that quantifies the density fluctuations of the initial state. We thereby identify a universality class of hyperuniform initial states whose dynamical variances coincide with the `quenched' cases studied previously; we also describe a continuous family of other classes among which equilibrated (or `annealed') initial conditions are but one family member. We verify our predictions through extensive Monte Carlo simulations.

accepted in Physical Review E (Letter)

References in corpus (16)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation
• Hyperuniformity of critical absorbing states
• Large Deviations in Single File Diffusion
• Ensemble Theory for Stealthy Hyperuniform Disordered Ground States
• Hyperuniform density fluctuations and diverging dynamic correlations in periodically driven colloidal suspensions
• Structure and dynamics in glass-formers: predictability at large length scales
• Diagnosing hyperuniformity in two-dimensional disordered jammed-packings of soft spheres
• Exact solution of the macroscopic fluctuation theory for the symmetric exclusion process
• Tracer dynamics in one dimensional gases of active or passive particles
• Generalised density profiles in single-file systems
• Field Theory of free Active Ornstein-Uhlenbeck Particles
• Current fluctuations in nanopores reveal the polymer-wall adsorption potential
• Macroscopic fluctuations of a driven tracer in the symmetric exclusion process
• Cumulant generating functions of a tracer in quenched dense symmetric exclusion processes
• Single file dynamics in soft materials

Cited by in corpus (21)

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• Effusion of stochastic processes on a line
• Structural properties of hard-disk fluids under single-file confinement
• Current fluctuations in an interacting active lattice gas
• Generalized disorder averages and current fluctuations in run and tumble particles
• Harmonic chain far from equilibrium: single-file diffusion, long-range order, and hyperuniformity
• Local time of a system of Brownian particles on the line with steplike initial condition
• Occupation time of a system of Brownian particles on the line with steplike initial condition
• Single-file diffusion in spatially inhomogeneous systems
• Fast Brownian cluster dynamics
• First-passage properties of the jump process with a drift. Two exactly solvable cases
• Scaling laws for single-file diffusion of adhesive particles
• Effect of initial conditions on current fluctuations in non-interacting active particles
• Uphill drift in the absence of current in single-file diffusion
• Emergent Gauge Symmetry in Active Brownian Matter
• Tracer dynamics in the active random average process
• Conserved densities of hard rods: microscopic to hydrodynamic solutions
• The distribution of the maximum of independent resetting Brownian motions
• Exact fluctuation and long-range correlations in a single-file model under resetting
• First-passage properties of the jump process with a drift. The general case
• Current fluctuations in finite-sized one-dimensional non-interacting passive and active systems