Information aging

We introduce the concept of information aging, and we propose a consistent definition of aging which reduces to the classic results for certain aging functions and whose limiting behavior are consistent. In the classic definition introduced by Shannon, the entropy of a random variable (RV) is an eternal quantity solely dependent on the probability mass function (PMF) of the RV itself. The basic premise of this paper is that the time elapsed between the moment of birth of a random event and the point in time when the event is observed is also of significance in so far as the information content of the event is concerned. In particular, we assume that the observation delay diminishes the information content of an event as measured by its eternal value given by the classic definition of entropy. Obviously, certain events are indeed of eternal value, while certain other events increase their information content with the passage of time. We consider the former type, although we provide definitions whereby the aging function is quite arbitrary and can accommodate all the cases noted