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Stationary uphill currents in locally perturbed zero-range processes.

Emilio N M Cirillo1, Matteo Colangeli2

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Uphill currents emerge when mass moves against its density gradient. Localized hopping rate asymmetry in one-dimensional zero-range processes (ZRPs) can drive this counter-intuitive diffusion, even in large systems.

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Physics
  • Complex Systems

Background:

  • Uphill currents, where mass transport opposes the density gradient, represent a counter-intuitive phenomenon in diffusion systems.
  • Understanding the mechanisms driving uphill currents is crucial for comprehending non-equilibrium statistical mechanics and complex system dynamics.

Purpose of the Study:

  • To investigate the emergence of uphill currents in stationary conditions within a theoretical framework.
  • To identify local perturbations that can induce mass diffusion against the density gradient in one-dimensional systems.

Main Methods:

  • Utilized one-dimensional zero-range processes (ZRPs) with local perturbations in hopping rates.
  • Analyzed stationary conditions and boundary injection rates to study mass transport dynamics.
  • Employed mathematical proofs for finite volumes and heuristic derivations for hydrodynamic behavior.

Main Results:

  • Demonstrated that a local asymmetry in hopping rates at a central lattice site can induce uphill currents.
  • Proved that this induced uphill diffusion can occur in arbitrarily large, finite volumes for fixed boundary injection rates.
  • Connected the local ZRP asymmetry to macroscopic matching conditions relevant for emergent phenomena.

Conclusions:

  • Local asymmetries in microscopic dynamics can drive macroscopic non-equilibrium phenomena like uphill currents.
  • The study provides a mechanism for generating counter-intuitive diffusion against density gradients in simplified models.
  • Findings offer insights into the relationship between local perturbations and emergent collective behavior in complex systems.