  The influence of a possible non zero chemical potential $\mu$ on the nature
of dark energy is investigated by assuming that the dark energy is a
relativistic perfect simple fluid obeying the equation of state (EoS),
$p=\omega \rho$ ($\omega <0, constant$). The entropy condition, $S \geq 0$,
implies that the possible values of $\omega$ are heavily dependent on the
magnitude, as well as on the sign of the chemical potential. For $\mu >0$, the
$\omega$-parameter must be greater than -1 (vacuum is forbidden) while for $\mu
< 0$ not only the vacuum but even a phantomlike behavior ($\omega <-1$) is
allowed. In any case, the ratio between the chemical potential and temperature
remains constant, that is, $\mu/T=\mu_0/T_0$. Assuming that the dark energy
constituents have either a bosonic or fermionic nature, the general form of the
spectrum is also proposed. For bosons $\mu$ is always negative and the extended
Wien's law allows only a dark component with $\omega < -1/2$ which includes
vacuum and the phantomlike cases. The same happens in the fermionic branch for
$\mu <0$. However, fermionic particles with $\mu >0$ are permmited only if $-1
< \omega < -1/2$. The thermodynamics and statistical arguments constrain the
EoS parameter to be $\omega < -1/2$, a result surprisingly close to the maximal
value required to accelerate a FRW type universe dominated by matter and dark
energy ($\omega \lesssim -10/21$).
