Approximate Hamiltonian Statistics in One-dimensional Driven Dissipative Many-Particle Systems

Abstract

This contribution presents a derivation of the steady-state distribution of velocities and distances of driven particles on a onedimensional periodic ring. We will compare two different situations: (i) symmetrical interaction forces fulfilling Newton's law of "actio = reactio" and (ii) asymmetric, forwardly directed interactions as, for example in vehicular traffic. Surprisingly, the steady-state velocity and distance distributions for asymmetric interactions and driving terms agree with the equilibrium distributions of classical many-particle systems with symmetrical interactions, if the system is large enough. This analytical result is confirmed by computer simulations and establishes the possibility of approximating the steady state statistics in driven many-particle systems by Hamiltonian systems. Our finding is also useful to understand the various departure time distributions of queueing systems as a possible effect of interactions among the elements in the respective queue [D. Helbing et al., Physica A 363, 62 (2006)].

11 pages, 7 figures, submitted to The European Physical Journal B

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• Theoretical vs. Empirical Classification and Prediction of Congested Traffic States
• The Intelligent Driver Model with Stochasticity -- New Insights Into Traffic Flow Oscillations
• Theoretical predictions for vehicular headways and their clusters
• Inner structure of vehicular ensembles and random matrix theory
• Inter-particle gap distribution and spectral rigidity of totally asymmetric simple exclusion process with open boundaries
• Walkers on the circle