Description:
We compute non-perturbative gluon spectral functions at finite temperature in quenched QCD with the maximum entropy method. We also provide a closed loop equation for the spectral function of the energy-momentum tensor in terms of the gluon spectral function. This setup is then used for computing the shear viscosity over entropy ratio $\eta/s$ in a temperature range from about $0.4\, T_c$ to $4.5\, T_c$. The ratio $\eta /s$ has a minimum at about $1.25\, T_c$ with the value of about 0.115. We also discuss extensions of the present results to QCD.