  We use quasiparticle anisotropic hydrodynamics to study the non-conformal and
non-extensive dynamics of a system undergoing boost-invariant Bjorken
expansion. To introduce nonextensivity, we use an underlying Tsallis
distribution with a time-dependent nonextensivity parameter $q$. By taking
moments of the quasiparticle Boltzmann equation in the relaxation-time
approximation, we obtain dynamical equations which allow us to determine the
time evolution of all microscopic parameters including $q$. We compare
numerical solutions for bulk observables obtained using the nonextensive
evolution with results obtained using quasiparticle anisotropic hydrodynamics
with a Boltzmann distribution function ($q \rightarrow 1$). We show that the
evolution of the temperature, pressure ratio, and scaled energy density, are
quite insensitive to which distribution function is assumed. However, we find
significant differences in the early-time evolution of the bulk pressure which
are observed for even small deviations from the Boltzmann distribution
function. Finally, we discuss the existence of non-conformal hydrodynamic
attractors for the longitudinal and transverse pressures, the bulk and shear
viscous corrections, and the nonextensivity parameter $q$.
