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We have used high-temperature ab initio molecular dynamic simulations to study the equation of state of orthorhombic MgSiO₃ perovskite under lower mantle pressure–temperature conditions. We have determined the Grüneisen parameter, γ, as a function of volume. Our state-of-the-art simulations, accurate to within 10%, resolve the long-standing controversy on thermal expansion (α) and Grüneisen parameter of MgSiO₃ perovskite. Under ambient conditions we find the values for α and γ of 1.86×10⁻⁵ K⁻¹ and 1.51, respectively, in excellent agreement with the latest experimental studies. Calculated elastic constants and the static equation of state at 0 K agree well with previous simulations. We have found no evidence for the high-temperature phase transitions of orthorhombic MgSiO₃ perovskite to cubic or tetragonal phases at mantle temperatures.