  The paper is devoted to the systematic derivation of nonperturbative
thermodynamics of quark-gluon plasma, on the basis of the background
perturbation theory. Vacuum background fields enter only in the form of field
correlators, which are known from lattice and analytic calculations. In the
lowest order in $\alpha_s$ the purely nonperturbative $sQGP$ thermodynamics is
expressed through single quark and gluon lines (single line approximation)
which are interacting nonperturbatively with vacuum fields and with other
lines. Nonperturbative EOS is obtained in terms (of the absolute value) of
fundamental (adjoint) Polyakov loop $L_{fund(adj)}$ and spatial string tension
$\sigma_s(T)$. In the lowest approximation the pressure for quarks (gluons) has
a simple factorized form $P_{q(g)}= P_{SB} L_{fund(adj)} ,$ where $ L_i$
describe the action of vacuum colorelectric fields on particle trajectory.
