When an active bath behaves as an equilibrium one

Active scalar baths consisting of active Brownian particles are characterized by a non-Gaussian velocity distribution, a kinetic temperature, and a diffusion coefficient that scale with the square of the active velocity <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>v</a:mi><a:mn>0</a:mn></a:msub></a:math>. While these results hold in overdamped active systems, inertial effects lead to normal velocity distributions, with kinetic temperature and diffusion coefficient increasing as <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mo>∼</b:mo><b:msubsup><b:mi>v</b:mi><b:mn>0</b:mn><b:mi>α</b:mi></b:msubsup></b:mrow></b:math> with <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mn>1</c:mn><c:mo><</c:mo><c:mi>α</c:mi><c:mo><</c:mo><c:mn>2</c:mn></c:mrow></c:math>. Remarkably, the late-time diffusivity and mobility decrease with mass. Moreover, we show that the equilibrium Einstein relation is asymptotically recovered with inertia. In summary, the inertial mass restores an equilibriumlike behavior. Published by the American Physical Society 2024