Nonperturbative effects in gluodynamics at T ≥ Tc

Contributions to gluon thermodynamics at temperature T > 0 due to a non-perturbative background field are calculated. The free energy is written as a double series in 1Nc and the strong coupling gs. The leading order contribution due to gluon loops in the nonperturbative background field contains explicitly the expectation value of the adjoint Polyakov line. The numerical value is taken from Monte Carlo calculations on a lattice. The results for the energy density and the pressure of the gluon gas strongly deviate from purely perturbative calculations and are in qualitative agreement with recent Monte Carlo lattice calculations.