Age and Time Operator of Evolutionary Processes

The Time Operator and Internal Age are intrinsic features of Entropy producing Innovation Processes. The innovation spaces at each stage are the eigenspaces of the Time Operator. The internal Age is the average innovation time, analogous to lifetime computation. Time Operators were originally introduced for Quantum Systems and highly unstable Dynamical Systems. The goal of this work is to present recent extensions of Time Operator theory to regular Markov Chains and Networks in a unified way and to illustrate the Non-Commutativity of Net Operations like Selection and Filtering in the context of Knowledge Networks.