Tagged active particle: probability distribution in a slowly varying external potential is determined by effective temperature obtained from the Einstein relation
arXiv:2102.11240 · doi:10.1063/5.0049239
Abstract
We derive a distribution function for the position of a tagged active particle in a slowly varying in space external potential, in a system of interacting active particles. The tagged particle distribution has the form of the Boltzmann distribution but with an effective temperature that replaces the temperature of the heat bath. We show that the effective temperature that enters the tagged particle distribution is the same as the effective temperature defined through the Einstein relation, i.e. it is equal to the ratio of the self-diffusion and tagged particle mobility coefficients. This shows that this effective temperature, which is defined through a fluctuation-dissipation ratio, is relevant beyond the linear response regime. We verify our theoretical findings through computer simulations. Our theory fails when an additional large length scale appears in our active system. This length scale is associated with long-wavelength density fluctuations that emerge upon approaching motility-induced phase separation.
arXiv comment10 pages, 13 figures
References in corpus (33)
- Active Particles in Complex and Crowded Environments
- Collective motion
- The Mechanics and Statistics of Active Matter
- Physics of Microswimmers - Single Particle Motion and Collective Behavior
- Energy flow, partial equilibration and effective temperatures in systems with slow dynamics
- Fluctuation-Dissipation: Response Theory in Statistical Physics
- How far from equilibrium is active matter?
- Violation of the fluctuation-dissipation theorem in glassy systems: basic notions and the numerical evidence
- Active matter
- A self-propelled particle in an external potential: is there an effective temperature?
- The effective temperature
- Effective Interactions in Active Brownian Suspensions
- Nonequilibrium dynamics and fluctuation-dissipation relation in a sheared fluid
- Multidimensional Stationary Probability Distribution for Interacting Active Particles
- Effective temperature of active matter
- Temperature in and out of equilibrium: a review of concepts, tools and attempts
- Extension of the Fluctuation-Dissipation theorem to the physical aging of a model glass-forming liquid
- Probing an nonequilibrium Einstein relation in an aging colloidal glass
- Fluctuation dissipation ratio in an aging Lennard-Jones glass
- How active forces influence nonequilibrium glass transitions
- From single-particle to collective effective temperatures in an active fluid of self-propelled particles
- Effective temperature in nonequilibrium steady states of Langevin systems with a tilted periodic potential
- Applicability of Effective Pair Potentials for Active Brownian Particles
- Efficient measurement of linear susceptibilities in molecular simulations: Application to aging supercooled liquids
- Effective temperatures in inhomogeneous passive and active bidimensional Brownian particle systems
- Violation of the Einstein relation in Granular Fluids: the role of correlations
- Evaluating linear response in active systems with no perturbing field
- Nonequilibrium Brownian motion beyond the effective temperature
- Active matter: quantifying the departure from equilibrium
- A stroll among effective temperatures in aging systems: limits and perspectives
- Active hard-spheres in infinitely many dimensions
- Generalized Fluctuation-Dissipation Relation and Effective Temperature upon Heating a Deeply Supercooled Liquid
- Tagged particle in a sheared suspension: effective temperature determines density distribution in a slowly varying external potential beyond linear response