  Statistical mechanics of a disordered system of cars on a single-lane road is
developed. Behaviour of cars is defined by conditional probability of car
velocity depending on the distance and velocity of the car ahead. A system
consisting of different cars is modelled by a system of two types of cars
differing in maximal velocity or efficiency of brakes. Starting from
conditional probabilities and using principle of maximum entropy, probability
densities of car velocities and headways are calculated. It is shown that the
first-order phase transition between free flow and congested traffic may be
driven by number of fast cars in a system of slow cars, and, as a rule,
admixture of cars of superior qualities does not increase but decreases the
total flow. In the system of cars with poor brakes platoons of cars of the same
velocity are formed. They are dissolved by a small addition of cars with good
brakes. Application of principle of maximum entropy was justified by comparing
the results with steady state properties of an equivalent kinetic model.
