  We perform an analysis of thermal SU(N) Yang-Mills theory in non-perturbative
regimes in the framework of Dyson-Swinger approach with a non-trivial ground
state involving Jacobi Elliptic functions. Basic thermodynamic observables such
as energy density and pressure have been derived analytically and compared with
well-known available lattice results. A good agreement has been found at low
temperatures providing a viable scenario of a gas of massive glue states
populating higher levels of the spectrum of the theory. At high-temperatures,
we observe that a scenario without glue states but consistent with a massive
scalar field shows an interesting agreement with lattice data. We discuss the
possibility of the results derived in this analysis to open up a novel pathway
for precision studies of phase transitions with false vacuum and cosmological
relics which depend upon QCD equation of state in strongly-coupled gauge
theories beyond lattice.
