Entropy and the Monitoring Problem

Abstract

Entropy is a well-known quantity that is used to describe verious phenomena in physics and information theory. Like energy or information, entropy cannot be measured directly and traditionally is used to describe the state of other physical quantities. Recently, a Russian physicist Anatoly Panchenkov introduced a new, more general, notion of entropy. In view of the principle of maximum P-entropy, a system evolves in the direction of its maximum lifespan , e.g., the life expectancy of humans, or business structures increases. An important feature of the differential equations that follow from the principle of maximum P-entropy is that they can be used to describe not only evolution, for example, as the equation of classical mechanics, but also events. In this thesis we will investigate how to employ the P-entropy to construct mathematical models that can be used in the theory of monitoring.