Effective Energy, Interactions And Out Of Equilibrium Nature Of Scalar Active Matter

TL;DR

This paper introduces a method to estimate the effective energy in scalar active matter systems, revealing how activity influences interaction range and phase separation, and linking non-equilibrium properties to emergent long-range interactions.

Contribution

It applies the Wavelet Conditional Renormalization Group method to estimate effective energy in active matter, uncovering the transition from short-range to long-range interactions with increasing activity.

Findings

Short-range interactions dominate at low activity

Long-range interactions emerge at high activity

Long-range interactions lead to micro-phase separation

Abstract

Estimating the effective energy, $E_\text{eff}$ of a stationary probability distribution is a challenge for non-equilibrium steady states. Its solution could offer a novel framework for describing and analyzing non-equilibrium systems. In this work, we address this issue within the context of scalar active matter, focusing on the continuum field theory of Active Model B+. We show that the Wavelet Conditional Renormalization Group method allows us to estimate the effective energy of active model B+ from samples obtained by numerical simulations. We investigate the qualitative changes of $E_\text{eff}$ as the activity level increases. Our key finding is that in the regimes corresponding to low activity and to standard phase separation the interactions in $E_\text{eff}$ are short-ranged, whereas for strong activity the interactions become long-ranged and lead to micro-phase separation. By analyzing the violation of Fluctuation-Dissipation theorem and entropy production patterns, which are directly accessible within the WCRG framework, we connect the emergence of these long-range interactions to the non-equilibrium nature of the steady state. This connection highlights the interplay between activity, range of the interactions and the fundamental properties of non-equilibrium systems.