Many important processes of industrial production and use of modern and functional materials are accompanied by phase transitions and hysteresis. Examples are: 1. Processes of condensation and crystallisation, including nucleation of droplets in vapour, crystal growth processes, precipitation in crystals or the evolution of unwanted bubbles in fluid flows. 2. Aging processes inducing damage, for example in modern solder joint materials. 3. Superelastic and hysteretic behavior of shape-memory alloys. 4. Storage and conversion of chemical and electrical energy. 5. Phenomena in high polymer materials.

In tight collaboration with users from industry, physics and chemistry existing as well as newly developed models are studied at WIAS regarding their practical relevance. The modelling of phase transitions and hysteresis may rely on statistical mechanics and stochastics of many-particle systems or is justified in the setting of phenomenological continuum thermodynamics. For example, classical and quantum many-particle systems are studied with respect to non-analytical behaviour of their free energies, and interacting random polymer chains and intermittent phenomena during random mass transport within random potentials are treated. The models of continuum thermodynamics often lead to coupled systems of non-linear partial differential equations or integro-differential equations, where free boundaries and hysteresis operators might occur.