Evolution of Complexity in Out-of-Equilibrium Systems by Time-Resolved or Space-Resolved Synchrotron Radiation Techniques

Out-of-equilibrium phenomena are attracting high interest in physics, materials science, chemistry and life sciences. In this state, the study of structural fluctuations at different length scales in time and space are necessary to achieve significant advances in the understanding of the structure-functionality relationship. The visualization of patterns arising from spatiotemporal fluctuations is nowadays possible thanks to new advances in X-ray instrumentation development that combine high-resolution both in space and in time. We present novel experimental approaches using high brilliance synchrotron radiation sources, fast detectors and focusing optics, joint with advanced data analysis based on automated statistical, mathematical and imaging processing tools. This approach has been used to investigate structural fluctuations in out-of-equilibrium systems in the novel field of inhomogeneous quantum complex matter at the crossing point of technology, physics and biology. In particular, we discuss how nanoscale complexity controls the emergence of high-temperature superconductivity (HTS), myelin functionality and formation of hybrid organic-inorganic supramolecular assembly. The emergent complex geometries, opening novel venues to quantum technology and to the development of quantum physics of living systems, are discussed.