Probing the limits of effective temperature consistency in actively driven systems

We investigate the thermodynamic properties of a single inertial probe driven into a nonequilibrium steady state by random collisions with self-propelled active walkers. The probe and walkers are confined within a gravitational harmonic potential. We evaluate the robustness of the effective temperature concept in this active system by comparing values of distinct, independently motivated definitions: a generalized fluctuation-dissipation relation, a kinetic temperature, and <i>via</i> a work fluctuation relation. Our experiments reveal that, under specific conditions, these independent measurements coincide over a wide range of system configurations, yielding a remarkably consistent effective temperature. Furthermore, we also identify regimes where this consistency breaks down, which delineates the fundamental limits of extending equilibrium-like thermodynamic concepts to athermal, actively driven systems.