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Journal of Statistical Physics

, Volume 42, Issue 3–4, pp 647–687 | Cite as

Thermodynamic treatment of nonphysical systems: Formalism and an example (Single-lane traffic)

  • H. Reiss
  • Audrey Dell Hammerich
  • E. W. Montroll
Articles

Abstract

An effort is made to introduce thermodynamic and statistical thermodynamic methods into the treatment of nonphysical (e.g., social, economic, etc.) systems. Emphasis is placed on the use of theentire thermodynamic framework, not merely entropy. Entropy arises naturally, related in a simple manner to other measurables, but does not occupy a primary position in the theory. However, the maximum entropy formalism is a convenient procedure for deriving the thermodynamic analog framework in which undetermined multipliers are thermodynamic-like variables which summarize the collective behavior of the system. We discuss the analysis of Levine and his coworkers showing that the maximum entropy formalism is the unique algorithm for achieving consistent inference of probabilities. The thermodynamic-like formalism for treating a single lane of vehicular traffic is developed and applied to traffic in which the interaction between cars is chosen to be a particular form of the “follow-the-leader” type. The equation of state of the traffic, the distributions of velocity and headway, and the various thermodynamic-like parameters, e.g., temperature (collective sensitivity), pressure, etc. are determined for an experimental example (Holland Tunnel). Nearest-neighbor and pair correlation functions for the vehicles are also determined. Many interesting and suggestive results are obtained,

Key words

Statistical thermodynamics social systems single-lane traffic collective behavior 

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Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • H. Reiss
    • 1
  • Audrey Dell Hammerich
    • 1
  • E. W. Montroll
    • 2
  1. 1.Department of Chemistry and BiochemistryUniversity of CaliforniaLos Angeles
  2. 2.Institute for Physical Science and TechnologyUniversity of MarylandCollege Park

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