  We present an $\textit{ab initio}$ study of the thermodynamic properties of
cubic CaSiO$_3$ perovskite (CaPv) over the pressure and temperature range of
the Earth's lower mantle. We compute the anharmonic phonon dispersions
throughout the Brillouin zone by utilizing the phonon quasiparticle approach,
which characterizes the intrinsic temperature dependence of phonon frequencies
and, in principle, captures full anharmonicity. Such temperature-dependent
phonon dispersions are used to calculate $\textit{ab initio}$ free energy in
the thermodynamic limit ($N \rightarrow \infty$) within the framework of the
phonon gas model. Accurate free energy calculations enable us to investigate
cubic CaPv's thermodynamic properties and thermal equation of state, where
anharmonic effects are demonstrated. The present methodology provides an
important theoretical approach for exploring phase boundaries, thermodynamic,
and thermoelastic properties of strongly anharmonic materials at high pressures
and temperatures.
