The van der Waals-like Phase Transition in the FRW Universe
  In this paper, we treat the Friedmann-Robertson-Walker (FRW) universe as a
thermodynamic system and study its thermodynamic properties especially the van
der Waals (vdW)-like (or $P$-$V$) phase transition. The thermodynamic pressure
$P$ is, almost for the first time, defined by the work density $W$ introduced
by Hayward. We further take the general relativity (GR) and the 4-dimensional
Einstein-Gauss-Bonnet (4D EGB) gravity as two examples to write down the
equations of state $P=P(V,T)$. We find that in GR, there is no vdW-like phase
transition for the FRW universe, while in the 4D EGB gravity the FRW universe
can have vdW-like phase transition, which to our best knowledge was never found
previously in the literature of the FRW thermodynamics. We also find that the
corresponding critical exponents are the same as those in the vdW system and
the mean field theory, so they satisfy the scaling laws.
