A microscopic theory for open systems is derived in terms of general manybody reduced density matrices and their fundamental properties. Correlated and coherent representations are obtained specifically identifying Yang’s concept of off‐diagonal long‐range order (ODLRO) and Coleman’s extreme case. The formulation is manifestly non‐linear with the microdynamical features given within the framework of complex dilations. Instead of going to the thermodynamic limit, we obtain through thermalization, certain universal, thermally activated, quantum fluctuations which are shown to appear as general (non‐abelian) Jordan forms. Some recent applications to high‐temperature superconductors (HTSC), the well‐established &mgr;SR‐experimental findings of Uemuraetal., the asymmetric quantum tunneling processes in HTSC/normal junctions, and the fractional Hall states (FQHE) of single‐layer and bi‐layer two‐dimensional structures are briefly discussed.