Statistical mechanics of non-hamiltonian systems: Traffic flow
arXiv:0709.0701 · doi:10.1088/1742-5468/2008/04/P04017
Abstract
Statistical mechanics of a small system of cars on a single-lane road is developed. The system is not characterized by a Hamiltonian but by a conditional probability of a velocity of a car for the given velocity and distance of the car ahead. Distribution of car velocities for various densities of a group of cars are derived as well as probabilities of density fluctuations of the group for different velocities. For high braking abilities of cars free-flow and congested phases are found. Platoons of cars are formed for system of cars with inefficient brakes. A first order phase transition between free-flow and congested phase is suggested.
12 pages, 6 figures, presented at TGF, Paris, 2007