  We investigate the impact of the Dark Energy Spectroscopic Instrument (DESI)
2024 data on dark energy scenarios. We thus analyze three typologies of models,
the first in which the cosmic speed up is related to thermodynamics, the second
associated with Taylor expansions of the barotropic factor, whereas the third
based on \emph{ad hoc} dark energy parameterizations. In this respect, we
perform Monte Carlo Markov chain analyses, adopting the Metropolis-Hastings
algorithm, of 12 models. To do so, we first work at the background, inferring
\emph{a posteriori} kinematic quantities associated with each model.
Afterwards, we obtain early time predictions, computing departures on the
growth evolution with respect to the model that better fits DESI data. We find
that the best model to fit data \emph{is not} the Chevallier-Polarski-Linder
(CPL) parametrization, but rather a more complicated log-corrected dark energy
contribution. To check the goodness of our findings, we further directly fit
the product, $r_d h_0$, concluding that $r_d h_0$ is anticorrelated with the
mass. This treatment is worked out by removing a precise data point placed at
$z=0.51$. Surprisingly, in this case the results again align with the
$\Lambda$CDM model, \emph{indicating that the possible tension between the
concordance paradigm and the CPL model can be severely alleviated}. We conclude
that future data points will be essential to clarify whether dynamical dark
energy is really in tension with the $\Lambda$CDM model.
