Entropy Measures, Maximum Entropy Principle and Emerging Applications

The last two decades have witnessed an enormous growth with regard to ap- plications of information theoretic framework in areas of physical, biological, engineering and even social sciences. In particular, growth has been spectac- ular in the field of information technology,soft computing,nonlinear systems and molecular biology. Claude Shannon in 1948 laid the foundation of the field of information theory in the context of communication theory. It is in- deed remarkable that his framework is as relevant today as was when he 1 proposed it. Shannon died on Feb 24, 2001. Arun Netravali observes "e;As if assuming that inexpensive, high-speed processing would come to pass, Shan- non figured out the upper limits on communication rates. First in telephone channels, then in optical communications, and now in wireless, Shannon has had the utmost value in defining the engineering limits we face"e;. Shannon introduced the concept of entropy. The notable feature of the entropy frame- work is that it enables quantification of uncertainty present in a system. In many realistic situations one is confronted only with partial or incomplete information in the form of moment, or bounds on these values etc. ; and it is then required to construct a probabilistic model from this partial information. In such situations, the principle of maximum entropy provides a rational ba- sis for constructing a probabilistic model. It is thus necessary and important to keep track of advances in the applications of maximum entropy principle to ever expanding areas of knowledge.