2018/01/12 by Lorenzo Caprini, Umberto Marini Bettolo Marconi, Angelo Vulpiani · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical mechanics #Diffusion and Search Dynamics #Mathematical analysis #Mathematics #Micro and Nano Robotics #Perturbation (astronomy) #Physics #Position (finance) #Quantum mechanics #Quartic function #Statistical physics #cond-mat.stat-mech
paper · pdf · doi:10.1088/1742-5468/aaa78c
published as Journal of Statistical Mechanics: Theory and Experiment 2018 · 16 pages
arxiv created 2018/01/12 · openalex publication_date 2018/03/01 · arxiv updated 2018/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract We study the non-equilibrium properties of non interacting active Ornstein–Uhlenbeck particles (AOUP) subject to an external nonuniform field using a Fokker–Planck approach with a focus on the linear response and time-correlation functions. In particular, we compare different methods to compute these functions including the unified colored noise approximation (UCNA). The AOUP model, described by the position of the particle and the active force acting on it, is usually mapped into a Markovian process, describing the motion of a fictitious passive particle in terms of its position and velocity, where the effect of the activity is transferred into a position-dependent friction. We show that the form of the response function of the AOUP depends on whether we put the perturbation on the position and keep unperturbed the active force in the original variables or perturb the position and maintain unperturbed the velocity in the transformed variables. Indeed, as a result of the change of variables the perturbation on the position becomes a perturbation both on the position and on the fictitious velocity. We test these predictions by considering the response for three types of convex potentials: quadratic, quartic and double-well potential. Moreover, by comparing the response of the AOUP model with the corresponding response of the UCNA model we conclude that although the stationary properties are fairly well approximated by the UCNA, the non equilibrium properties are not, an effect which is not negligible when the persistence time is large.