Fluctuation-Dissipation Relations in Active Matter Systems

We investigate the non-equilibrium character of self-propelled particles through the studyof the linear response of the active Ornstein-Uhlenbeck particle (AOUP) model. We express the linearresponse in terms of correlations computed in the absence of perturbations, proposing a particularlycompact and readable fluctuation-dissipation relation (FDR): such an expression explicitly separatesequilibrium and non-equilibrium contributions due to self-propulsion. As a case study, we considernon-interacting AOUP confined in single-well and double-well potentials. In the former case, we alsounveil the effect of dimensionality, studying one-, two-, and three-dimensional dynamics. We showthat information about the distance from equilibrium can be deduced from the FDR, putting inevidence the roles of position and velocity variables in the non-equilibrium relaxation.