Time-dependent Ginzburg-Landau equation in a car-following model considering the driver's physical delay

► The formulation of the thermodynamic theory for the jamming transition has been presented. ► We get the time-dependent Ginzburg-Landau (TDGL) equation from the car-following model. ► We show the connection between the TDGL equation and the modified Korteweg-de Vries equation describing the traffic jam.