Statistical Mechanics predicts the thermodynamic properties of macroscopic amounts of materials by averaging over an ensemble of states of a larger number of microscopic constituents. Tow powerful tools in Statistical Mechanics are numerical simulations and Renormalization Group Theory (RGT). Important concepts are the notion of scaling and of universality, which is a common behavior that can be ascribed to a class of systems which are very different on the microscopic level. IN RGT, scaling leads to the emergence of power laws which are universal over a class that includes different systems.

Soft Statistical Mechanics is the application of Statistical Mechanics to soft matter, a severely neglected area. Soft matter has so far attracted very little attention in Statistical Mechanics, because it is typically extremely difficult to treat due to its microscopic complexity and irregularity. The constituents of soft matter are typically a liquid or a gas combined with fibers, bubbles, droplets or other large objects, in an arrangement with usually no symmetry, no simple interactions, no known way to decouple modes and no clear scale. Certainly, soft matter appears to be not friendly territory for Statistical Mechanics.

However, there are also signs of hope, for example in the area of soft glassy rheology. When measuring the the complex vsicoelastic modulus as a function of frequency, one sees two encouraging features: The first is the existence of various power laws, which can extend over orders of magnitude, which suggest some kind of limited scale invariance. The second is the emergence of universality, when two very different systems (say, filaments suspended in solution in one case and an emulsion in the other) show a similar dependency between the modulus and the frequency.

The occurance of universality opens the door for an interesting opportunity: Instead of modelling a real and very difficult system, we can instead model a much simpler system that shows the same behaviour but allows for a useful model. Such a system does not even need to exist in reality, as long as it is in the same universality class as a system we are actually interested in.

Once such a model system has been formulated, it can be attacked using numerical simulations and RGT, the classical power tools of Statistical Mechanics. Once the system is understood, universality allows us to apply the results to a real and typically much more complicated system, which may otherwise not be solved. The central task is then to design the model system.

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