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Nonequilibrium steady state for harmonically confined active particles.

Naftali R Smith1, Oded Farago2

  • 1Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, 8499000, Israel.

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Summary
This summary is machine-generated.

We analyzed particle motion in a harmonic trap with active noise. Large deviations from typical behavior follow a non-Boltzmann distribution, scaling with a large-deviation function as noise correlation time approaches zero.

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Area of Science:

  • Statistical physics
  • Non-equilibrium systems
  • Soft matter physics

Background:

  • Studying the steady-state distribution of particles in confined potentials is crucial for understanding complex systems.
  • Active noise introduces non-equilibrium dynamics, deviating from classical Boltzmann statistics.

Purpose of the Study:

  • To investigate the full nonequilibrium steady-state distribution of a damped particle in a harmonic potential under active noise.
  • To characterize large deviation behavior and its dependence on noise properties.

Main Methods:

  • Analysis of the particle's position distribution P_{st}(X).
  • Approximation of short-correlated active noise as white Gaussian thermal noise for typical fluctuations.
  • Derivation of the large-deviation function s(X) in the limit of vanishing correlation time (τ_{c}→0).

Main Results:

  • Typical fluctuations follow a Boltzmann distribution with an effective temperature.
  • Large deviations exhibit a non-Boltzmann steady-state distribution.
  • A universal scaling behavior P_{st}(X)∼e^{-s(X)/τ_{c}} was identified for short correlation times.
  • The large-deviation function s(X) was derived for general active noise and calculated for telegraphic noise.

Conclusions:

  • The study reveals distinct behaviors for typical and large fluctuations in active systems.
  • The derived scaling law provides a framework for understanding deviations from equilibrium in driven systems.
  • Exact results for telegraphic noise offer a concrete example of the theoretical findings.