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Phase Transitions in Stochastic Models of Flow

In: Traffic and Granular Flow’05

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  • Martin R. Evans

    (The University of Edinburgh, SUPA, School of Physics)

Abstract

Summary In this talk I will review some very simple models of nonequilibrium systems known as the ‘Asymmetric Exclusion Process’ and the ‘Zero-Range Process’. These involve particles hopping stochastically on a lattice and thus form stochastic models of flow. Systems driven out of equilibrium can often exhibit behaviour not seen in systems in thermal equilibrium - for example phase transitions in one-dimensional systems. I shall show how examples of such transitions may be interpreted as jamming transitions in the context of traffic flow. More generally I shall discuss other instances of the condensation transition which is the phenomenon of a finite fraction of the driven conserved quantity condensing into a small spatial region. Criteria for the occurrence of condensation may be formulated and the detailed properties of the condensate such as its fluctuations have recently been elucidated.

Suggested Citation

  • Martin R. Evans, 2007. "Phase Transitions in Stochastic Models of Flow," Springer Books, in: Andreas Schadschneider & Thorsten Pöschel & Reinhart Kühne & Michael Schreckenberg & Dietrich E. Wol (ed.), Traffic and Granular Flow’05, pages 447-459, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-47641-2_41
    DOI: 10.1007/978-3-540-47641-2_41
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