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Complex systems manifest emergent properties that can in no way be reduced to the properties of the constituent parts. Such a priori unexpected aspects include symmetry-breaking bifurcations and self-organization under nonequilibrium conditions, the coexistence of order and disorder in chaotic dynamics and stochastic processes, or self-similar processes leading to the formation of fractals, as observed in many natural systems. Our research activities aim at understanding such complex phenomena on the basis of mathematical descriptions provided by the underlying physico-chemical laws. For this purpose multilevel approaches, from microscopic dynamics up to macroscopic balance equations via mesoscopic schemes in terms of stochastic processes are developed. Our expertise combines methods from nonlinear dynamics, bifurcation theory, complexity characterization, irreversible thermodynamics, nonequilibrium statistical mechanics, transport theory, stochastic processes, classical and quantum mechanics. These methods and expertise serve as a jumping off point for selected applications to nanosciences, surface science, chemical physics, biophysics, and neurosciences.

Recent achievements include fundamental relationships establishing that irreversible properties find their origin in the breaking of time-reversal symmetry in the statistical description of nonequilibrium systems, and that dynamical order manifests itself out of equilibrium. These results shed new light on information generation and information processing in complex systems.

The Service is part of the Interdisciplinary Centre for Nonlinear Phenomena and Complex Systems of ULB.