The equations of state (EOS) of Iridium are, for the first time, obtained by solving the high-dimension integral of partition function based on a recently developed approach of ultrahigh efficiency and precision without any artificial parameter, and the deviation of 0.25% and 1.52% from the experiments was achieved respectively for the isobaric EOS in a temperature range of 300 K-2500 K and the isothermal EOS at 300 K up to 300 GPa. Specific comparisons show that the deviation of EOS based on harmonic approximation even including anharmonic effect, manifests worse than ours by several times or even one order of magnitude, indicating that ensemble theory is the very approach to understand the thermodynamic properties of condensed matter.
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