  High-energy phenomena presenting strong dynamical correlations, long-range
interactions and microscopic memory effects are well described by nonextensive
versions of the canonical Boltzmann-Gibbs statistical mechanics. After a brief
theoretical review, we introduce a class of generalized heat-bath algorithms
that enable Monte Carlo lattice simulations of gauge fields on the nonextensive
statistical ensemble of Tsallis. The algorithmic performance is evaluated as a
function of the Tsallis parameter q in equilibrium and nonequilibrium setups.
Then, we revisit short-time dynamic techniques, which in contrast to usual
simulations in equilibrium present negligible finite-size effects and no
critical slowing down. As an application, we investigate the short-time
critical behaviour of the nonextensive hot Yang-Mills theory at q- values
obtained from heavy-ion collision experiments. Our results imply that, when the
equivalence of statistical ensembles is obeyed, the long-standing universality
arguments relating gauge theories and spin systems hold also for the
nonextensive framework.
