Long-ranged correlations in large deviations of local clustering

TL;DR

This paper studies how local biases in particle systems induce long-range correlations in clustering behavior, revealing system-wide responses and scaling laws through macroscopic fluctuation theory.

Contribution

It demonstrates that a bias on a single particle causes system-wide long-range correlations, with analysis based on macroscopic fluctuation theory and scaling relationships.

Findings

Long-range correlations span the entire system.

Dynamical free energy scales non-trivially with system size.

Biasing two particles affects the system's clustering response.

Abstract

In systems of diffusing particles, we investigate large deviations of a time-averaged measure of clustering around one particle. We focus on biased ensembles of trajectories, which realise large-deviation events. The bias acts on a single particle, but elicits a response that spans the whole system. We analyse this effect through the lens of Macroscopic Fluctuation Theory, focussing on the coupling of the bias to hydrodynamic modes. This explains that the dynamical free energy has non-trivial scaling relationships with the system size, in 1 and 2 spatial dimensions. We show that the long-ranged response to a bias on one particle also has consequences when biasing two particles.