  Recently, a covariant formulation of non-equilibrium phenomena in the context
of General Relativity was proposed in order to explain from first principles
the observed accelerated expansion of the Universe, without the need for a
cosmological constant, leading to the GREA theory. Here, we confront the GREA
theory against the latest cosmological data, including type Ia supernovae,
baryon acoustic oscillations, the cosmic microwave background (CMB) radiation,
Hubble rate data from the cosmic chronometers and the recent $H_0$
measurements. We perform Markov Chain Monte Carlo analyses and a Bayesian model
comparison, by estimating the evidence via thermodynamic integration, and find
that when all the aforementioned data are included, but no prior on $H_0$, the
difference in the log-evidence is $\sim -9$ in favor of GREA, thus resulting in
overwhelming support for the latter over the cosmological constant and cold
dark matter model ($\Lambda$CDM). When we also include priors on $H_0$, either
from Cepheids or the Tip of the Red Giant Branch measurements, then due to the
tensions with CMB data the GREA theory is found to be statistically equivalent
with $\Lambda$CDM.
