WIAS Preprint No. 724, (2002)

Towards rigorous micro-macro transitions: The microscopic oscillator motion



Authors

  • Dreyer, Wolfgang
  • Herrmann, Michael

2010 Mathematics Subject Classification

  • 70F45 82C22 35L65

Keywords

  • Conservation laws, Many particle systems, Micro-macro transitions, Multiscale problems, Young measures

Abstract

The atomic chain whose dynamics evolve according to Newton's equations of motion serves as a simple microscopic many-particle system for an analysis of the macroscopic or thermodynamic limit. If the interaction potential has a sufficient strong repulsive part, it is possible to create a special microscopic motion, that we call oscillator motion, which is simpler as the classical thermal motion. However, also the oscillator motion leads to temperature, a Gibbs equation and an entropy. In the current paper we derive the thermodynamics for the oscillator motion without the subtle replacement of the many-particle sytem by a single equation of motion as it is done in [4]. Furthermore we introduce a different mathematical setting for micro-macro transitions as in [4], which is better suited for a rigorous treatment.

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