We compute the Hugoniot curves of both neat TATB and its detonation products mixture using atomistic simulation tools. To compute the Hugoniot states, we adapted our "Sampling Constraints in Average" (SCA) method (Maillet et al., Applied Math. Research eXpress 2008, 2009) to Monte-Carlo simulations. For neat TATB, we show that the potential proposed by Rai (Rai et al., J. Chem. Phys. 129, 2008) is not accurate enough to predict the Hugoniot curve and requires some optimization of its parameters. Concerning detonation products, thermodynamic properties at chemical equilibrium are computed using a specific RxMC method (Bourasseau et al., Phys. Chem. Chem. Phys. 13, 2011) taking into account the presence of carbon clusters in the fluid mixture. We show that this explicit description of the solid phase immersed in the fluid phase modifies the chemical equilibrium.