Generic feature of future crossing of phantom divide in viable $f(R)$
  gravity models
  We study the equation of state for dark energy and explicitly demonstrate
that the future crossings of the phantom divide line $w_{\mathrm{DE}}=-1$ are
the generic feature in the existing viable $f(R)$ gravity models. We also
explore the future evolution of the cosmological horizon entropy and illustrate
that the cosmological horizon entropy oscillates with time due to the
oscillatory behavior of the Hubble parameter. The important cosmological
consequence is that in the future, the sign of the time derivative of the
Hubble parameter changes from negative to positive in these viable $f(R)$
gravity models.
