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Correlations in nonequilibrium diffusive systems.

P L Garrido1

  • 1Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada, Spain.

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Summary
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We investigated nonequilibrium correlation functions in diffusive systems. The study reveals that fluctuations are dominated by local equilibrium, even under driven, nonequilibrium conditions, up to second order.

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Area of Science:

  • Statistical Physics
  • Non-equilibrium Systems
  • Mesoscopic Physics

Background:

  • Understanding the behavior of systems driven far from equilibrium is crucial in statistical physics.
  • Diffusive systems with equilibrium reference states (DSe) provide a framework to study these phenomena.
  • Stationary nonequilibrium states are characterized by persistent deviations from equilibrium.

Purpose of the Study:

  • To analyze the properties of stationary nonequilibrium two-body correlation functions in diffusive systems.
  • To decompose these correlations into equilibrium and nonequilibrium (excess) components.
  • To derive and solve differential equations for the correlation's excess using perturbative expansion.

Main Methods:

  • Mesoscopic description using M locally conserved continuum fields and Langevin equations.
  • Definition of correlation's excess C[over ¯](x,z) representing nonequilibrium behavior.
  • Perturbative expansion around the equilibrium state to solve for C[over ¯].

Main Results:

  • The first-order correlation's excess C[over ¯]^{(1)} is zero for M=1 and long-range or zero for M>1.
  • Fluctuations, defined as space integrals of C[over ¯]^{(1)}, are surprisingly always zero.
  • Fluctuations are dominated by local equilibrium up to second order in the perturbative expansion.

Conclusions:

  • The study provides a detailed analysis of nonequilibrium correlations and their fluctuations.
  • Results indicate that local equilibrium significantly influences fluctuations even in driven systems.
  • Explicit derivations for d=1, 2 and for M=2 cases offer specific insights into system dynamics.