Generalized energy equipartition in harmonic oscillators driven by active baths

TL;DR

This paper investigates the dynamics of colloidal beads in active bacterial baths, revealing a generalized energy equipartition with two effective temperatures governing different directions.

Contribution

It introduces a model combining thermal and active noise to describe colloidal dynamics, extending the equipartition theorem to active baths.

Findings

Identification of two effective temperatures in active bath dynamics

Experimental and numerical validation of the generalized equipartition

Demonstration of anisotropic effective temperatures along different potential directions

Abstract

We study experimentally and numerically the dynamics of colloidal beads confined by a harmonic potential in a bath of swimming E. coli bacteria. The resulting dynamics is well approximated by a Langevin equation for an overdamped oscillator driven by the combination of a white thermal noise and an exponentially correlated active noise. This scenario leads to a simple generalization of the equipartition theorem resulting in the coexistence of two different effective temperatures that govern dynamics along the flat and the curved directions in the potential landscape.