A Statistical Mechanics Approach to Continuum Mechanics

Continuum mechanics and atomistic models can be related starting from statistical mechanics by coarse graining methods and scaling limits. I will present some results in this direction which specify in a mathematically rigorous fashion the range of scales where a continuum description emerges and how randomness and thermal noise may be added to the deterministic laws of continuum mechanics to capture effects from the underlying atomistic structure.

Free energy functionals and related variational problems with issues like degeneracy of minimizers and phase transitions, Wulff problem and optimal shape of a droplet, can be rigorously derived from statistical mechanics with Kac potentials in a scaling limit. Finite scale effects where randomness and large deviations play an important role are then also discussed.

Errico Presutti, Universita di Roma "Tor Vergata", Italy


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