  We have revealed statistical physics of synchronized traffic flow that is
governed by a spatiotemporal competition between S$\rightarrow$F and
S$\rightarrow$J instabilities (where F, S, and J denote, respectively, the free
flow, synchronized flow, and wide moving jam traffic phases). A probabilistic
analysis of synchronized flow based on simulations of a cellular automaton
model in the framework of three-phase traffic theory is made. This
probabilistic analysis shows that there is a finite range of the initial
space-gap between vehicles in synchronized flow within which during a chosen
time for traffic observation either synchronized flow persists with probability
$P_{\rm S}$, or an S$\rightarrow$F transition occurs with probability $P_{\rm
SF}$, or else an S$\rightarrow$J transition occurs with probability $P_{\rm
SJ}$. Space-gap dependencies of the probabilities $P_{\rm S}$, $P_{\rm SF}$,
and $P_{\rm SJ}$ have been found. The statistical features of synchronized flow
found for a homogeneous road remain qualitatively for a road with a bottleneck.
However, rather than nuclei for S$\rightarrow$F and S$\rightarrow$J
instabilities occur at random road locations of the homogeneous road, due to a
permanent non-homogeneity introduced by the bottleneck, nuclei for initial
S$\rightarrow$F and S$\rightarrow$J instabilities appear mostly at the
bottleneck.
