Improved actions for QCD thermodynamics on the lattice

Finite cut-off effects strongly influence the thermodynamics of lattice regularized QCD at high temperature in the standard Wilson formulation. We analyze the reduction of finite cut-off effects in formulations of the thermodynamics of SU(N) gauge theories with three different O(a^2) and O(a^4) improved actions. We calculate the energy density and pressure on finite lattices in leading order weak coupling perturbation theory (T\rightarrow \infty) and perform Monte Carlo simulations with improved SU(3) actions at non-zero g^2. Already on lattices with temporal extent N_\tau=4 we find a strong reduction of finite cut-off effects in the high temperature limit, which persists also down to temperatures a few times the deconfinement transition temperature.