The akimotoite to perovskite phase transition of MgSiO3 is shown by first principles calculations to have a negative Clapeyron slope, consistent with experimental observations. The origin of the negative slope, i.e., the increase of entropy across the transformation, can be attributed to the larger density of states of low frequency vibrations in the perovskite phase. Such vibrations consist of 1) magnesium displacements and 2) octahedral rotations, with the larger magnesium coordination and larger Mg-O bond lengths, as well as a lower degree of polyhedral connectivity accounting for the existence of low frequency modes. The larger density of states in perovskite in this regime accounts also for the increase in other thermodynamic properties across the phase transition. This ab initio calculation of a solid-solid phase boundary provides new insights into our ability to predict high pressure-temperature transformations by first principles.