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

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.

References in corpus (15)

• Motility-Induced Phase Separation
• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• Statistical Mechanics of Active Ornstein Uhlenbeck Particles
• Tunable long range forces mediated by self-propelled colloidal hard spheres
• Motility-Induced Microphase and Macrophase Separation in a Two-Dimensional Active Brownian Particle System
• Non-reciprocity across scales in active mixtures
• Play. Pause. Rewind. Measuring local entropy production and extractable work in active matter
• A review of active matter reviews
• Synthetic Lagrangian Turbulence by Generative Diffusion Models
• Disorder-Induced Long-Ranged Correlations in Scalar Active Matter
• Critical active dynamics is captured by a colored-noise driven field theory
• Disordered boundaries destroy bulk phase separation in scalar active matter
• Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production
• Deep learning probability flows and entropy production rates in active matter
• Inclusions, Boundaries and Disorder in Scalar Active Matter