Spin glass and the interactions of congestion and emissions: An exploratory step

This paper models traffic congestion formation on highways and roads by recognizing the centrality of dynamical systems and using concepts from complexity theory as imbedded in the spin glasses analogue. Further, it explores the concept of how an increase in air pollution caused by vehicle exhaust emission can be traced to traffic congestion, specifically to the acceleration/deceleration of vehicles on the roads. First, spin glass is introduced and then by applying the two-dimensional x − y Ising model and defining a Hamiltonian (based on Edwards-Anderson and Mattis models of spin glass systems) for a system of vehicles on the road, derivations are made of the specific friction of congestion and the bulk modulus of congestion using the Gibbs-Boltzmann statistic. Similarly using the interactions of vehicles with each other and the resulting accelerations and decelerations of vehicles as the basis for exhaust emissions, derivations are made of a specificity of exhaust emissions. These are analogues to the entropy models of thermodynamics. This series of derivations serves as an analytical model for detecting incidents of congestion and increase in air pollution due to exhaust emissions in transportation systems.