Abstract
We investigate the non-equilibrium character of self-propelled particles through the study of the linear response of the active Ornstein–Uhlenbeck particle (AOUP) model. We express the linear response in terms of correlations computed in the absence of perturbations, proposing a particularly compact and readable fluctuation–dissipation relation (FDR): such an expression explicitly separates equilibrium and non-equilibrium contributions due to self-propulsion. As a case study, we consider non-interacting AOUP confined in single-well and double-well potentials. In the former case, we also unveil the effect of dimensionality, studying one-, two-, and three-dimensional dynamics. We show that information about the distance from equilibrium can be deduced from the FDR, putting in evidence the roles of position and velocity variables in the non-equilibrium relaxation.
Highlights
The fluctuation–dissipation relations (FDR) played a pivotal role in the development of non-equilibrium statistical mechanics
We investigate the non-equilibrium character of self-propelled particles through the study of the linear response of the active Ornstein–Uhlenbeck particle (AOUP) model
Our study provides an explicit extension of the generalized FDR to non-equilibrium systems of active matter that are numerically checked in many cases of interest, in particular, the case of the quartic potential explored for one, two, and three-dimensional systems and the case of a double-well potential
Summary
The fluctuation–dissipation relations (FDR) played a pivotal role in the development of non-equilibrium statistical mechanics. Examples of FDR of class B are derived from the Malliavin weight sampling [11], or the Novikov theorem [12], which have been intensively employed in the context of glassy physics and represent a powerful tool to calculate the susceptibility and, the so-called effective temperature of a system [4,13] In this approach, the FDR involves correlations with the noise and the physical meaning of these terms remain often difficult to catch. In the spirit of minimal modeling, these systems could be described through simple stochastic dynamics that resembles that of passive colloids except for the addition of a coarse-grained time-dependent force, often called self-propulsion or active force [21,22] This force replaces the microscopic details of the system that, in general, are related to complicate internal mechanisms of energy transduction and involve an intrinsic source of strong deviation from thermodynamic equilibrium.
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