The Einstein effective temperature can predict the tagged active particle density

Area of Science:

• Statistical Mechanics
• Soft Matter Physics
• Active Matter Physics

Background:

• Interacting active particles exhibit unique statistical properties distinct from equilibrium systems.
• Understanding particle behavior in external potentials is crucial for active matter dynamics.
• Effective temperature is a key concept for characterizing non-equilibrium systems.

Purpose of the Study:

• To derive a position distribution function for a tagged particle in a system of interacting active particles.
• To investigate the concept of effective temperature in active matter systems.
• To validate theoretical predictions using computational simulations.

Main Methods:

• Derivation of a distribution function for a tagged active particle.
• Analysis of the Boltzmann distribution with an effective temperature.
• Comparison of effective temperature from distribution function and Einstein relation.
• Verification through computer simulations of interacting active particles.

Main Results:

• The tagged particle distribution follows a Boltzmann-like form with an effective temperature.
• The effective temperature is consistent with the ratio of self-diffusion and mobility coefficients.
• This effective temperature is relevant beyond the linear response regime.
• The theory breaks down in the presence of large length scales, such as those near motility-induced phase separation.

Conclusions:

• The effective temperature provides a unified description for tagged particle distributions and transport properties in active matter.
• The fluctuation-dissipation ratio defines an effective temperature applicable beyond linear response.
• The emergence of large-scale density fluctuations can limit the applicability of the derived theory.