We computed equations of state of hydrogen in warm dense matter regime by using DPIMC method. In large part of the regime, pressure difference between DPIMC and RPIMC is less than 10%. In low temperature regime, some difference beyond 20%. We pointed out two clerical errors in pressure of RPIMC. In dissociation and ionization regime, pressures of DPIMC lie between results of TF and TFC model. In dissociation regime, the largest pressure difference between DPIMC and RPIMC is 15%. In ionization regime, pressures of DPIMC are agree with RPIMC. In low density regime, internal energies of DPIMC are close to those of RPIMC, less than those of QMD and those of IG model. In high density regime, pressures of DPIMC lie between results of TFC and IG model, internal energies of DPIMC less than those of IG model.

Application of simulated annealing method in chemical free energy model to search for chemical composition of equilibrium state is proposed. Due to the random "thermal" fluctuations introduced by simulated annealing method, the difficulty associated with sensitivity of result to initial values is removed. Moreover, in the regime of first order phase transition where stable state and meta-stable state coexist, the stable state can always be obtained. As an example, chemical free energy model improved by simulated annealing method is applied to the equation of state for fluid helium, which demonstrates the plasma phase transition induced by pressure ionization.

Equation of state of detonation products for HMX explosive is calculated. Detonation velocity and detonation pressure at CJ point are calculated as initial density of HMX explosive is 1.90 g·cm^-3. It shows satisfactory agreement with experimental data. Mole numbers of various detonation products are predicted and compared with results of BKW and LJD. Pressure, γ and mole numbers of detonation products along CJ adiabatic expansion path are given. They are helpful for understanding phenomenon of detonation.