Active fluctuations in the harmonic chain: phonons, entropons and velocity correlations

Abstract

Non-equilibrium random fluctuations of non-thermal nature are a salient feature of active matter. In this work, we consider the collective excitations of active systems at high density, focusing on a one-dimensional chain of elastically coupled inertial particles, whose activity is modeled with an Ornstein-Uhlenbeck process. Their excitation spectrum shows the presence of two kinds of fluctuations: the first ones are thermally excited phonons analogous to those of a passive crystal while the second ones have been termed entropons because associated with the entropy production due to the active forces. These two types of fluctuations show different properties: in fact, only entropons generate spatial velocity correlations and fail to satisfy a standard fluctuation-response relation. We derive the exact expression for the equal-time velocity and displacement correlations as well as for the structure factor and in each case identify the phonon and entropon contributions. Finally, we investigate the dynamical properties of the excitations in terms of steady-state two-time correlations, such as the intermediate scattering function and the mean-square displacement, and show that both phonon and entropon fluctuations are characterized by a long wavelength overdamped regime and a short wavelength underdamped regime. In the large persistence case, entropons decay slower than phonons, and in general, activity tends to suppress the oscillations typical of the underdamped regime.