QCD inequalities for the nucleon mass and the free energy of baryonic matter

The positivity of the integrand of certain Euclidean space functional integrals implies that the free energy per unit volume for QCD with a baryon chemical potential $\mu_B$ (and zero isospin chemical potential) is greater than the free energy with isospin chemical potential $\mu_I = (2 \mu_B)/N_c$ (and zero baryon chemical potential). This relation implies a bound on the nucleon mass: there exists a particle X in QCD such that $M_N \ge (N_c m_X)/(2 I_X)$ where $m_X$ is the mass and of the particle and $I_X$ is its isospin.