Application of thermodynamics to driven systems
arXiv:cond-mat/0606509 · doi:10.1140/epjb/e2007-00182-7
Abstract
Application of thermodynamics to driven systems is discussed. As particular examples, simple traffic flow models are considered. On a microscopic level, traffic flow is described by Bando's optimal velocity model in terms of accelerating and decelerating forces. It allows to introduce kinetic, potential, as well as total energy, which is the internal energy of the car system in view of thermodynamics. The latter is not conserved, although it has certain value in any of two possible stationary states corresponding either to fixed point or to limit cycle in the space of headways and velocities. On a mesoscopic level of description, the size n of car cluster is considered as a stochastic variable in master equation. Here n=0 corresponds to the fixed-point solution of the microscopic model, whereas the limit cycle is represented by coexistence of a car cluster with n>0 and free flow phase. The detailed balance holds in a stationary state just like in equilibrium liquid-gas system. It allows to define free energy of the car system and chemical potentials of the coexisting phases, as well as a relaxation to a local or global free energy minimum. In this sense the behaviour of traffic flow can be described by equilibrium thermodynamics. We find, however, that the chemical potential of the cluster phase of traffic flow depends on an outer parameter - the density of cars in the free-flow phase. It allows to distinguish between the traffic flow as a driven system and purely equilibrium systems.
9 pages, 6 figures. Eur. Phys. J. B (2007) to be published
References in corpus (13)
- Traffic and Related Self-Driven Many-Particle Systems
- Statistical Physics of Vehicular Traffic and Some Related Systems
- Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
- Brownian Particles far from Equilibrium
- Criterion for phase separation in one-dimensional driven systems
- Critical phenomena and universal dynamics in one-dimensional driven diffusive systems with two species of particles
- Long-lived states in synchronized traffic flow. Empirical prompt and dynamical trap model
- Probabilistic Description of Traffic Breakdowns
- Zero range model of traffic flow
- Determination of Interaction Potentials in Freeway Traffic from Steady-State Statistics
- How human drivers control their vehicle
- The thermodynamic dual structure of linear-dissipative driven systems
- Two effective temperatures in traffic flow models: analogies with granular flow