Microscopic Time-Reversibility and Macroscopic Irreversibility — Still a Paradox?

  • Harald A. Posch
  • Christoph Dellago
  • William G. Hoover
  • Oyeon Kum


Microscopic time reversibility and macroscopic irreversibility are a paradoxical combination. This was first observed by J. Loschmidt in 1876 and was explained, for conservative systems, by L. Boltzmann the following year. Both these features are also present in modern simulations of classic many-body systems in steady nonequilibrium states. We illustrate them here for the simplest possible models, a continuous one-dimensional model of field-driven diffusion, the so-called driven Lorentz gas or Galton Board, and an ergodic time-reversible dissipative map.


Lyapunov Exponent Strange Attractor Singularity Spectrum Lyapunov Spectrum Steady Nonequilibrium State 
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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Harald A. Posch
    • 1
  • Christoph Dellago
    • 1
  • William G. Hoover
    • 2
  • Oyeon Kum
    • 2
  1. 1.Institute for Experimental PhysicsUniversity of ViennaAustria
  2. 2.Department of Physics Lawrence Livermore National Laboratory and Department of Applied ScienceUniversity of California at Davis/LivermoreLivermoreUSA

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