Nested Stochastic Resetting: Nonequilibrium Steady States and Exact Correlations.

Area of Science:

• Statistical physics
• Complex systems
• Nonequilibrium dynamics

Background:

• Stochastic resetting is a key mechanism for creating nonequilibrium steady states.
• Understanding correlations in many-particle systems is challenging.
• Unilateral interactions in diffusive processes are common in nature.

Purpose of the Study:

• To analytically derive the steady-state statistics of nested stochastic resetting processes.
• To calculate exact steady-state two-point correlations between interacting processes.
• To provide a tractable framework for studying unilateral interactions in random processes.

Main Methods:

• Analysis of nested stochastic resetting processes.
• Derivation of stationary distributions and moments.
• Mapping to ordering statistics of random counting processes.

Main Results:

• Exact analytical solutions for steady-state distributions and moments.
• Exact calculation of steady-state two-point correlations.
• Demonstration of tractable correlations in a many-particle nonequilibrium system.

Conclusions:

• The developed framework offers a model-independent approach for random processes with unilateral interactions.
• Results provide insights into statistical properties and correlations in nonequilibrium systems.
• Potential applications include modeling lossy information propagation.