A thermodynamic approach to holographic dark energy

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.