  It is understood that congestion in traffic can be interpreted in terms of
the instability of the equation of dynamic motion. The evolution of a traffic
system from an unstable or metastable state to a globally stable state bears a
strong resemblance to the phase transition in thermodynamics. In this work, we
explore the underlying physics of the traffic system, by examining closely the
physical properties and mathematical constraints of the phase transitions
therein. By using a mesoscopic approach, one entitles the catastrophe model the
same physical content as in the Landau's theory, and uncovers its close
connections to the instability of the equation of motion and to the transition
between different traffic states. In addition to the one-dimensional
configuration space, we generalize our discussions to the higher-dimensional
case, where the observed temporal oscillation in traffic flow data is
attributed to the curl of a vector field. We exhibit that our model can
reproduce the main features of the observed fundamental diagram including the
inverse-$\lambda$ shape and the wide scattering of congested traffic data. When
properly parameterized, the main feature of the data can be reproduced
reasonably well either in terms of the oscillating congested traffic or in
terms of the synchronized flow.
