  The characterization of the distance from equilibrium is a debated problem in
particular in the treatment of experimental signals. If the signal is a
1-dimensional time-series, such a goal becomes challenging. A paradigmatic
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 significative differences with respect to an equilibrium
process. Exploiting the presence of two relevant time-scales and non-Gaussian
velocity increments, we quantify the breakdown of time-reversal asymmetry,
which would vanish in the case of a 1D 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 the granular bath particles. Our model reproduces the experiment in a
range of densities, from dilute to moderately dense, with a meaningful
dependence of the parameters on the density. We believe the framework proposed
here opens the way to a more consistent and meaningful treatment of
out-of-equilibrium and dissipative systems.
