Anharmonic thermodynamic properties and phase boundary across the postperovskite transition in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>MgSi</mml:mi><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math>

To address the effects of lattice anharmonicity across perovskite to post-perovskite transition in MgSiO$_3$, we conduct calculations using phonon quasiparticle (PHQ) approach. The PHQ is based on \textit{ab initio} molecular dynamics and, principle, captures full anharmonicity. Free energies thermodynamic limit ($N \rightarrow \infty$) are computed temperature-dependent dispersions within gas model. Systematic results anharmonic properties and phase boundary reported. Both local density approximation (LDA) generalized gradient (GGA) performed provide confident constraints these properties. Anharmonic demonstrated by comparing with those obtained quasiharmonic (QHA). inadequacy QHA indicated its overestimation thermal expansivity Gr\"{u}neisen parameter converged isochoric heat capacity high-temperature limit. has a Clapeyron slope ($dP/dT$) that increases temperature. This result contrasts nearly zero curvature boundary. Anharmonicity bends lower temperatures at high pressures. Implications for double-crossing mantle geotherm discussed.