Towards rigorous micro-macro transitions: The microscopic oscillator motion
- Dreyer, Wolfgang
- Herrmann, Michael
2010 Mathematics Subject Classification
- 70F45 82C22 35L65
- Conservation laws, Many particle systems, Micro-macro transitions, Multiscale problems, Young measures
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 . Furthermore we introduce a different mathematical setting for micro-macro transitions as in , which is better suited for a rigorous treatment.