  By generalizing the recently developed path integral molecular dynamics for
identical bosons and fermions, we consider the finite-temperature thermodynamic
properties of fictitious identical particles with a real parameter $\xi$
interpolating continuously between bosons ($\xi=1$) and fermions ($\xi=-1$).
Through general analysis and numerical experiments we find that the average
energy may have good analytical property as a function of this real parameter
$\xi$, which provides the chance to calculate the thermodynamical properties of
identical fermions by an extrapolation with a simple polynomial function after
accurately calculating the thermodynamic properties of the fictitious particles
for $\xi\geq 0$. Using several examples, it is shown that our method can
efficiently give accurate energy values for finite-temperature fermionic
systems. Our work provides a chance to circumvent the fermion sign problem for
some quantum systems.
