Statistical and Biological Physics
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Complex systems in biology, chemistry and physics are in general nonlinear and far from equilibrium, intricately coupled and heterogeneous. Why then do they not simply collapse, run out of control or become chaotic? The canonical theory of pattern formation deals with nonlinear systems that are near a global equilibrium state and where nonlinear interactions have a stabilizing effect. However, in the real world this is rarely the case: collective effects in biological, ecological, or economic systems, can lead to sudden, dramatic changes in the dynamics more

Entropy and topology are major determinants of the complex dynamics and emergent behaviour of soft matter systems. In particular, the correct description of the release of topological constraints still poses a major challenge in almost any such system. In a series of seminal papers, de Gennes, Edwards and Doi formulated the reptation theory of entangled polymer solutions, which has become a paradigm in the field of soft-matter physics. Not only did the theory introduce new physical concepts, it was also highly successful in explaining many of the unusual properties and collective phenomena exhibited by materials comprised of flexible polymers. Importantly, reptation theory is a mean-field theory, as it essentially replaces the effect of the complicated many-body interaction between the polymer chains by a constraining tube along which polymers move in a snake-like fashion. more