Revealing the Nonequilibrium Nature of a Granular Intruder: The Crucial Role of Non-Gaussian Behavior

The characterization of the distance from equilibrium is a debated problem in particular in the treatmentof experimental signals. If the signal is a one-dimensional time series, such a goal becomes challenging. Aparadigmatic example is the angular diffusion of a rotator immersed in a vibro-fluidized granular gas. Here,we experimentally observe that the rotator's angular velocity exhibits significant differences with respect toan equilibrium process. Exploiting the presence of two relevant timescales and non-Gaussian velocityincrements, we quantify the breakdown of time-reversal asymmetry, which would vanish in the case of a1D Gaussian process. We deduce a new model for the massive probe, with two linearly coupled variables,incorporating both Gaussian and Poissonian noise, the latter motivated by the rarefied collisions with thegranular bath particles. Our model reproduces the experiment in a range of densities, from dilute tomoderately dense, with a meaningful dependence of the parameters on the density. We believe theframework proposed here opens the way to a more consistent and meaningful treatment of out-ofequilibrium and dissipative systems.