Dear Colleagues,

How important is uncertainty in the life of a human being? Certainly, an existence in which everything is deterministic is not worth living.

In 1948, Claude Shannon developed the general concept of entropy, a “measure of uncertainty”, a fundamental cornerstone of information theory, coming out from the idea of quantifying how much information there is in a message. In his paper “A Mathematical Theory of Communication”, he set out to mathematically quantify the statistical nature of “lost information” in phone-line signals while working at Bell Telephone Laboratories.

Entropy in information theory is directly analogous to entropy in statistical thermodynamics.

In information theory, the entropy of a random variable is the average level of “information”, “uncertainty” or “surprise” inherent in the variable’s possible outcomes.

The entropy was originally a part of his theory of communication, in which a data communication system is composed of three elements: a source of data, a communication channel, and a receiver. In Shannon’s theory, the “fundamental problem of communication” is for the receiver to be able to identify what data were generated by the source, based on the signal it receives through the channel. Thus, the basic idea is that the “informational value” of a communicated message depends on the degree to which the content of the message is surprising.

Entropy has relevance to other areas of mathematics. The definition comes from a set of axioms establishing that entropy should be a measure of how “surprising” the average outcome of a variable is. For a continuous random variable, differential entropy is analogous to entropy.

If an event is very probable, it is uninteresting when that event happens as expected; hence, transmission of such a message carries very little new information. However, if an event is unlikely to occur, it is much more informative to learn if the event happened or will happen.

In the last decades, several new measures of information and of discrimination have been defined and studied, and it is clear that many other ones (with applications in different fields) will be introduced. This Special Volume has the aim of enriching notions related to measures of discrimination.

Prof. Dr. Maria Longobardi
Dr. Francesco Buono
Guest Editors

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• Measures of Information II in Entropy (11 articles)
• Measures of Information in Entropy (10 articles)