What is entropy? A perspective from games of chance.

Abstract

The crucial role of channels in physics and information theory motivates the task of characterizing the entropy, or uncertainty, of a channel. Games of chance become a natural candidate for this task, as a system's performance in a gambling game depends solely on the uncertainty of its output. In this work, we construct families of games that induce preorders corresponding to majorization, conditional majorization, and channel majorization. Finally, we provide operational interpretations for all preorders, show the relevance of these results to dynamical resource theories, and find the only asymptotically continuous classical channel entropy.