  We study in detail the influence of different chemical potentials (baryon,
charged, strange, and neutrino) on how and how fast a free gas of quarks in the
zero-temperature limit reaches the conformal limit. We discuss the influence of
non-zero masses, the inclusion of leptons, and different constraints, such as
charge neutrality, zero-net strangeness, and fixed lepton fraction. We also
investigate for the first time how the symmetry energy of the system under some
of these conditions approaches the conformal limit. Finally, we briefly discuss
what kind of corrections are expected from perturbative QCD as one goes away
from the conformal limit.
