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The characterization of the distance from equilibrium is a debated problem inparticular in the treatment of experimental signals. If the signal is a1-dimensional time-series, such a goal becomes challenging. A paradigmaticexample is the angular diffusion of a rotator immersed in a vibro-fluidizedgranular gas. Here, we experimentally observe that the rotator's angularvelocity exhibits significative differences with respect to an equilibriumprocess. Exploiting the presence of two relevant time-scales and non-Gaussianvelocity increments, we quantify the breakdown of time-reversal asymmetry,which would vanish in the case of a 1D Gaussian process. We deduce a new modelfor the massive probe, with two linearly coupled variables, incorporating bothGaussian and Poissonian noise, the latter motivated by the rarefied collisionswith the granular bath particles. Our model reproduces the experiment in arange of densities, from dilute to moderately dense, with a meaningfuldependence of the parameters on the density. We believe the framework proposedhere opens the way to a more consistent and meaningful treatment ofout-of-equilibrium and dissipative systems.

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