Low-energy theorems of QCD and bulk viscosity at finite temperature and baryon density in a magnetic field

The nonperturbative QCD vacuum at finite temperature and a finite baryon density in an external magnetic field is studied. Equations relating nonperturbative condensates to the thermodynamic pressure for $T\mathrm{\ne }0$, $\mu_q \neq 0$and$H\neq 0$ are obtained, and low-energy theorems are derived. A bulk viscosity $\zeta (T,\mu ,H)$ is expressed in terms of basic thermodynamical quantities describing the quark-gluon matter at $T\mathrm{\ne }0$, ${\mu }_q\mathrm{\ne }0$, and $H\mathrm{\ne }0$. Various limiting cases are also considered.