The need for alternative information measures

In 1948 Shannon advanced information theory (IT) as a new branch of mathematics and a powerful tool for understanding the intricacies of the communication process. Nine years later Jaynes’ conceived the maximum entropy principle and was able to shed with it much light onto statistical mechanics and thermodynamics. Shannonʹs logarithmic information measure, the MaxEnt protagonist, was successfully connected with the thermodynamic entropy. Since 1988 a new project, called nonextensive thermostatistics (NET), came into being after the pioneering work by Tsallis and collaborators. It has achieved today a remarkable degree of success, amid a not small degree of controversy. It is also a MaxEnt construction but uses a different information measure in the leading role. We advance here some epistemological considerations on the proper place of any information measure within a theoretical physics’ construct in order put NET into a more solid conceptual framework.