Statistical mechanics of non-hamiltonian systems: Traffic flow

TL;DR

This paper develops a statistical mechanics framework for traffic flow on a single-lane road, analyzing velocity distributions, phase transitions, and platoon formation in non-Hamiltonian systems.

Contribution

It introduces a novel non-Hamiltonian statistical mechanics approach to model traffic flow, capturing phase transitions and platoon formation.

Findings

Identifies free-flow and congested phases at high braking abilities.

Shows formation of car platoons with inefficient brakes.

Suggests a first order phase transition between phases.

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.