A simple model for the evolutionary emergence of novel properties

In contradistinction to classical theories quantum mechanics sharply distinguishes between potential and essential properties of a system. The potential properties of a quantal system are described by a set of observables. The subset of those observables that commute with all others is called the center of observables and represents the essential properties, i.e. the properties actualized in each state of the system. If a quantum system is open its time evolution can change the center and turn merely potential properties into essential ones and vice versa. The temporal behavior of such a system clearly shows the characteristics of evolutionary change; quantum mechanics can describe how novel properties emerge in the course of time. This is in clear contrast to the behavior of Turing- or Belousov-Zhabotinskii type models where the evolutionary change only produces a refinement of an existing essential property and not something really new. - As an illustration we present a simple model with non-trivial evolutionary behavior.