  We explore the thermodynamics of the gluon plasma in SU(3) Yang-Mills theory
emerging from the non-trivial spatial dynamics of valence gluons. The lattice
data suggest that these gluons interact with each other linearly at large
spatial separations. At high temperatures, valence gluons should reproduce the
pressure of the non-interacting Stefan-Boltzmann plasma along with the leading
perturbative correction. These properties of valence gluons can be modeled in
terms of the integral over their trajectories. We calculate such a world-line
integral analytically and obtain the pressure and the interaction measure
$(\varepsilon-3p)/T^4$ of the gluon plasma. Additionally, we account for the
contributions of stochastic background fields to these thermodynamic
quantities. The results turn out to be in a good agreement with the
corresponding lattice data. In particular, the lattice-simulated peak of the
interaction measure near the deconfinement critical temperature is reproduced.
