The temperature-dependent Yang-Mills trace anomaly as a function of the mass gap

The trace anomaly or, equivalently, the interaction measure is the important thermodynamic quantity/observable, since it is very sensitive to the non-perturbative effects in the gluon plasma. It has been calculated and its analytic and asymptotic properties have been investigated with the combined force of analytic and lattice approaches to $SU(3)$ Yang-Mills (YM) quantum gauge theory at finite temperature. The first one is based on the effective potential approach for composite operators properly generalized to finite temperature. This makes it possible to introduce into this formalism a dependence on the mass gap $\Delta^2$, which is responsible for the large-scale dynamical structure of the QCD ground state. The gluon plasma pressure as a function of the mass gap adjusted by this approach to the corresponding lattice data is shown to be a continuously growing function of temperature $T$ in the whole temperature range $[0, \infty)$ with correct Stefan-Boltzmann limit at very hight temperature. The corresponding trace anomaly has finite jump discontinuity at some characteristic temperature $T_c = 266.5 \ MeV$ with latent heat $\epsilon_{LH}= 1.41$. This is a firm evidence of the first-order phase transition in $SU(3)$ pure gluon plasma