  We check the dynamical and observational features of four typologies of
logotropic dark energy models, leading to a \emph{thermodynamic cosmic speed
up} fueled by a single fluid that unifies dark energy and dark matter. We first
present two principal Anton-Schmidt fluids where the Gr\"uneisen parameter
$\gamma_{\rm G}$ is free to vary and then fixed to the special value
$\gamma_{\rm G}=\tfrac{5}{6}$. We also investigate the pure logotropic model,
corresponding to $\gamma_{\rm G}=-\frac{1}{6}$. Finally, we propose a new
logotropic paradigm that works as a generalized logotropic fluid, in which we
split the role of dark matter and baryons. We demonstrate that the logotropic
paradigms may present drawbacks in perturbations, showing a negative adiabatic
sound speed which make perturbations unstable. The Anton-Schmidt model with
$\gamma_{\rm G}=\frac{5}{6}$ is ruled out while the generalized logotropic
fluid seems to be the most suitable one, albeit weakly disfavored than the
$\Lambda$CDM model. We combine low- and higher-redshift domains through
experimental fits based on Monte Carlo Markov Chain procedures, taking into
account supernovae Ia catalogue, Hubble measurements and $\sigma_8$ data
points. We consider two model selection criteria to infer the statistical
significance of the four models. We conclude there is statistical advantage to
handle the Anton-Schmidt fluid with the Gr\"uneisen parameter free to vary
and/or fixed to $\gamma_{\rm G}=-\frac{1}{6}$. The generalized logotropic fluid
indicates suitable results, statistically favored than the other models, until
the sound speed is positive, becoming unstable in perturbations elsewhere. We
emphasize that the $\Lambda$CDM paradigm works statistically better than any
kinds of logotropic and generalized logotropic models, while the
Chevallier-Polarski-Linder parametrization is statistically comparable with
logotropic scenarios.
