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, $��_H$. 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.

12 pages, 10 figures