  We study the thermodynamics of helical matter, namely quark matter in which a
net helicity, $n_H$, is in equilibrium. Interactions are modeled by the
renormalized quark-meson model with two flavors of quarks. Helical density is
described within the grand-canonical ensemble formalism via a chemical
potential, $\mu_H$. We study the transitions from the normal quark matter and
hadron gas to the helical matter, drawing the phase diagram at zero
temperature. We study the restoration of chiral symmetry at finite temperature
and show that the net helical density softens the transition, moving the
critical endpoint to lower temperature and higher baryon chemical potential.
Finally, we discuss briefly the effect of a rigid rotation on the helical
matter, in particular on the fluctuations of $n_H$, and show that these are
enhanced by the rotation.
