Long-ranged correlations in large deviations of local clustering

Area of Science:

• Statistical Physics
• Complex Systems
• Non-equilibrium Dynamics

Background:

• Understanding particle clustering is crucial in various physical systems.
• Investigating large deviations reveals rare but significant system behaviors.
• Macroscopic fluctuation theory provides a framework for non-equilibrium systems.

Purpose of the Study:

• To analyze large deviations of particle clustering around a single particle.
• To understand how a local bias on one particle affects the entire system.
• To explore the consequences of biasing two particles in such systems.

Main Methods:

• Focus on biased ensembles of trajectories to realize large-deviation events.
• Application of macroscopic fluctuation theory.
• Analysis of the coupling between bias and hydrodynamic modes.

Main Results:

• A local bias on a single particle induces a long-ranged response across the system.
• Dynamical free energy exhibits non-trivial scaling with system size in 1 and 2 dimensions.
• Biasing two particles also leads to observable consequences.

Conclusions:

• The study elucidates the collective response to local perturbations in diffusing particle systems.
• Findings highlight the importance of hydrodynamic modes in mediating system-wide effects.
• The research provides insights into the statistical mechanics of non-equilibrium systems.