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Three-body problem for Langevin dynamics with different temperatures.

Michael Wang1, Alexander Y Grosberg1

  • 1Department of Physics and Center for Soft Matter Research, New York University, 726 Broadway, New York, New York 10003, USA.

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Summary
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Three-particle interactions in Brownian systems do not follow simple Boltzmann distributions with an effective temperature. The steady-state behavior of particle pairs depends on the third particle, revealing non-equilibrium dynamics.

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Area of Science:

  • Statistical Mechanics
  • Non-Equilibrium Physics
  • Soft Matter Physics

Background:

  • Brownian particle systems at different temperatures model out-of-equilibrium microscopic systems.
  • Previous analytical studies focused on two-particle interactions, yielding Boltzmann-like distributions with an effective temperature in the dilute limit.

Purpose of the Study:

  • To investigate if two-particle interaction results can be extended to three-particle interactions for three-particle distributions.
  • To determine if three-particle distributions in such systems can be Boltzmann-like with an effective temperature.

Main Methods:

  • Analytical investigation of three-particle interactions.
  • Consideration of the solvable case of pairwise quadratic interactions.

Main Results:

  • Unlike two-particle distributions, three-particle distributions are generally not Boltzmann-like with an effective temperature.
  • The steady-state distribution of any two particles within a triplet is influenced by the third particle's properties and interactions.

Conclusions:

  • The extension of two-particle equilibrium-like distributions to three-particle systems in non-equilibrium settings is not straightforward.
  • The findings reveal unexpected behaviors in steady-state distributions due to the influence of the third particle, deviating from equilibrium predictions.