Steady-state moments under resetting to a distribution

Area of Science:

• Statistical Physics
• Nonlinear Dynamics
• Stochastic Processes

Background:

• Stochastic resetting introduces a mechanism to reset a system's state to a specific distribution.
• Understanding nonequilibrium steady states is crucial for various physical and biological systems.
• Previous studies often focused on specific resetting distributions or dynamics.

Purpose of the Study:

• To investigate the properties of nonequilibrium steady states emerging from stochastic resetting to a distribution.
• To establish a general framework for calculating steady-state moments in such systems.
• To derive explicit solutions for specific physical models.

Main Methods:

• Analytical derivation of steady-state moment expressions.
• Development of a general formula relating system moments to resetting distribution moments.
• Application to Brownian and run-and-tumble particle dynamics in a harmonic potential.
• Numerical simulations for verification.

Main Results:

• Steady-state moments are shown to be a linear combination of moments of the resetting distribution.
• The coefficients of this linear combination are universal, depending only on the underlying dynamics.
• Closed-form expressions for all moments are derived for Brownian and run-and-tumble particles.
• Numerical simulations confirm the analytical results with excellent agreement.

Conclusions:

• Stochastic resetting to a distribution leads to universal properties in steady-state moments.
• The derived framework simplifies the analysis of complex stochastic systems with resetting.
• The findings provide a powerful tool for studying diverse physical phenomena involving resetting.