  The key problem of statistical physics standing over one hundred years is how
to exactly calculate the partition function (or free energy) of many-body
interaction systems, which severely hinders application of the theory for
realistic systems. Here we present a novel approach that works at least four
orders faster than state-of-the-art algorithms to the problem and can be
applied to predict thermal properties of large molecules or macroscopic
condensed matters via \emph{ab initio} calculations.The method was demonstrated
by C$_{60}$ molecules, solid and liquid copper (up to $\sim 600$GPa), solid
argon, graphene and silicene on substrate, and the derived internal energy or
pressure is in a good agreement with the results of vast molecular dynamics
simulations in a temperature range up to $2500$K, achieving a precision at
least one order higher than previous methods. And, for the first time, the
realistic isochoric equation of state for solid argon was reproduced directly
from the partition function.
