Exploring Different Temperature Definitions for an Athermal Tracer in an Active Bath: Out-of-Equilibrium Effects and Mass Dependence

The notion of temperature in out-of-equilibrium systems is still elusive. Here, we explore three different temperature definitions for an athermal tracer immersed in a out-of-equilibrium bath of active Brownian particles, with which it interacts solely through collisions. Temperatures are, respectively, defined from velocity fluctuations, the fluctuation-dissipation theorem and a heat fluctuation theorem, and we find their values to increase with the tracer’s mass following sigmoidal trends, the first two sharing similar values, the one defined from the fluctuation theorem showing lower ones. Notably, these trends are reminiscent of the trend of the kinetic temperature of a single free active particle as function of its mass. Using thus the latter as fit functional form, we interpret the tracer as effectively behaving like a single free active particle with the same mass but lower persistence time or activity amplitude.