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Lower Current Large Deviations for Zero-Range Processes on a Ring.

Paul Chleboun1, Stefan Grosskinsky2, Andrea Pizzoferrato2

  • 11Department of Statistics, University of Oxford, Oxford, UK.

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|April 1, 2020
PubMed
Summary
This summary is machine-generated.

We investigated large deviations in particle flow for asymmetric zero-range processes. A dynamic transition was found, where low current fluctuations shift from traveling waves to particle condensation.

Keywords:
CondensationCurrent fluctuationsLarge deviationsZero-range process

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Area of Science:

  • Statistical Mechanics
  • Stochastic Processes
  • Non-equilibrium Physics

Background:

  • Totally asymmetric zero-range processes (TAZRP) are fundamental models in non-equilibrium statistical mechanics.
  • Understanding current fluctuations and large deviations is crucial for characterizing system dynamics.
  • Previous work applied Jensen-Varadhan approach to exclusion processes, motivating its use here.

Purpose of the Study:

  • To study lower large deviations for the current in TAZRP on a ring with a concave current-density relation.
  • To identify and characterize a dynamic transition in the attainment of large current deviations.
  • To provide a general characterization of the rate function for these deviations.

Main Methods:

  • Utilizing the Jensen and Varadhan approach, previously applied to exclusion processes.
  • Analyzing current fluctuations through traveling wave density profiles.
  • Investigating non-entropic weak solutions of the hyperbolic scaling limit.
  • Employing numerical simulations with a cloning algorithm to support findings.

Main Results:

  • Identified a dynamic transition where large deviations below a threshold are attained by condensed profiles, not just non-entropic weak solutions.
  • Established that condensed profiles involve a non-zero fraction of particles accumulating on a single site.
  • Derived a general characterization of the rate function for current fluctuations.
  • Presented detailed results for four distinct examples of jump rates (constant, decreasing, unbounded sublinear, asymptotically linear).

Conclusions:

  • The study reveals a novel dynamic transition in the large deviation behavior of TAZRP currents.
  • Condensed profiles represent a distinct mechanism for achieving large deviations, particularly at lower current values.
  • The generalized rate function characterization and specific examples offer valuable insights into TAZRP dynamics.