Thermodynamic theory for the jamming transition in traffic flow

A thermodynamic theory is formulated for describing the phase transition and critical phenomenon occurring in traffic flow. We derive the time-dependent Ginzburg-Landau (TDGL) equation from the car-following model. We find the thermodynamic potential for traffic flow where the headway and the inverse of the delay time correspond respectively to order parameter and temperature. It is shown that the coexisting curve and spinodal line are given respectively by the first and second derivatives of the potential with order parameter (the headway). We prove that the jamming transition is the first-order transition below the critical point and the metastable region exists between the coexisting curve and spinodal line. We show the connection between TDGL equation and the modified Korteweg–de Vries equation describing the traffic jam. We also compare the nonlinear analysis result with the simulation. It is shown that the coexisting curve is consistent with the simulation result.