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Dynamically emergent correlations in Brownian particles subject to simultaneous non-Poissonian resetting protocols
Gabriele de Mauro1, Marco Biroli1, Satya N Majumdar1
1Université Paris-Saclay, CNRS, LPTMS, Univ. Paris-Sud, 91405 Orsay, France.
Physical Review. E
|February 20, 2026
Summary
Stochastic resetting creates correlations in Brownian particle systems, leading to a tunable, strongly correlated nonequilibrium stationary state (NESS). This allows exact calculation of particle distributions and observables for various resetting protocols.
Area of Science:
- Statistical Physics
- Nonlinear Dynamics
- Many-Body Systems
Background:
- Independent Brownian particles exhibit simple dynamics.
- Stochastic resetting introduces non-Markovian behavior and can alter system states.
- Understanding many-body systems with complex dynamics is crucial for statistical physics.
Purpose of the Study:
- To investigate the effects of simultaneous stochastic resetting on a 1D gas of N Brownian particles.
- To analyze the emergence of correlations and a nonequilibrium stationary state (NESS).
- To derive analytical expressions for particle distributions and physical observables under general resetting protocols.
Main Methods:
- Modeling a 1D gas of N independent Brownian particles with simultaneous stochastic resetting.
- Utilizing a general waiting-time distribution ψ(τ) for inter-reset times.
- Exploiting the renewal structure of resetting dynamics for analytical derivations.
- Analyzing large-N scaling behaviors for different resetting protocols.
Main Results:
- Simultaneous resetting dynamically generates correlations between particles.
- These correlations lead to a strongly correlated nonequilibrium stationary state (NESS).
- Explicit analytical expressions for particle joint distributions in the NESS were derived.
- The NESS exhibits a conditionally independent and identically distributed structure, enabling exact computation of observables.
- Universal large-N scaling behaviors were identified for various observables.
Conclusions:
- Stochastic resetting can be used as a control mechanism to generate tunable, solvable, strongly correlated NESS.
- The choice of inter-reset distribution ψ(τ) significantly impacts system correlations and steady-state properties.
- This work provides a framework for analyzing complex many-body systems with stochastic control.
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