  We propose a method to relate the holographic minimal information density to
the de Broglie's wavelength at a given universe temperature $T$. To figure this
out, we assume that the thermal length of massive and massless constituents
represents the cut-off scale of the holographic principle. To perform our
analysis, we suppose two plausible universe volumes, i.e. the adiabatic and the
horizon volumes, i.e. $V \propto a^3$ and $V \propto H^{-3}$ respectively,
assuming zero spatial curvature. With these choices in mind, we evaluate the
thermal lengths for massive and massless particles and we thus find two
cosmological models associated to late and early cosmological epochs. We
demonstrate that both models depend upon a free term $\beta$ which enters the
temperature parametrization in terms of the redshift $z$. For the two
treatments, we show evolving dark energy terms which can be compared with the
$\omega$CDM quintessence paradigm when the barotropic factor takes the formal
values: $\omega_0=-\frac{1}{3}(2+\beta)$ and $\omega_0=-\frac{1}{3}(1+2\beta)$
respectively for late and early eras. From our analyses, we candidate the two
models as viable alternatives to dark energy determined from thermodynamics in
the field of the holographic principle.
