Time-dependent Ginzburg–Landau equation for the jamming transition in traffic flow

We present the thermodynamic theory describing the phase transition and critical phenomenon in traffic flow. We derive the time-dependent Ginzburg–Landau (TDGL) equation through the modified Korteweg–de Vries (KdV) equation from the car following model, using the perturbation method. We find the thermodynamic potential for the jamming transition. It is shown that the coexisting and spinodal lines are obtained, respectively, from the first and second derivatives of the potential. We prove that the jamming transition is the first-order phase transition below the critical point and metastability exists between the coexisting and spinodal lines.