Nonequilibrium steady state of trapped active particles.

Area of Science:

• Statistical Mechanics
• Soft Matter Physics
• Non-equilibrium Systems

Background:

• Active particles exhibit complex dynamics due to self-propulsion and noise.
• Understanding the steady-state distribution of confined active particles is crucial for predicting their behavior.
• Existing models often simplify noise correlations, limiting applicability.

Purpose of the Study:

• To derive the nonequilibrium steady-state distribution for an overdamped active particle in an external potential.
• To investigate deviations from Boltzmann statistics in the tails of the distribution.
• To exactly calculate the large-deviation function for active particle position in the small noise correlation time limit.

Main Methods:

• Analysis of an overdamped particle model with general active noise (e.g., run-and-tumble, active Brownian).
• Focusing on the limit of small correlation time (τ→0) of the active noise.
• Relating the large-deviation function to the rate function of the free active particle in one dimension (d=1).

Main Results:

• Identified that typical fluctuations follow a Boltzmann distribution with an effective temperature.
• Discovered that the tails of the steady-state distribution deviate from Boltzmann behavior, scaling as Pst(X)∼e^{-s(X)/τ}.
• Derived an exact expression for the large-deviation function s(X) for arbitrary potentials in d=1.
• Extended the findings to higher dimensions (d>1) under rotational symmetry.

Conclusions:

• The study provides an exact solution for the large-deviation behavior of confined active particles.
• The findings highlight the importance of noise correlation time in determining the full steady-state distribution.
• This work offers a theoretical framework for understanding anomalous diffusion and extreme events in active matter systems.