Twenty Years of Kaniadakis Entropy: Current Trends and Future Perspectives

Kaniadakis’ entropy, proposed about two decades ago, is briefly considered in this 2 editorial that introduces this special issue of ENTROPY. This special issue contains 15 papers 3 dedicated to Kaniadakis’ entropy, and a summary of these papers is given. Here, the new entropy 4 is introduced starting from the Kaniadakis deformation, which is compared with the well-known 5 Euler deformation. Then Kaniadakis’ exponential and logarithmic functions are introduced and 6 the axiomatic structure of Kaniadakis’ statistical mechanics is emphasized. The editorial also 7 contains a list of more than 250 papers written in the last twenty-five years up to January 2025 8 by various authors from different parts of the world, dealing exclusively with the foundations, 9 mathematical formalism, and applications of Kaniadakis’ theory. This list should not be considered 10 as a complete bibliography on Kaniadakis statistics and includes only the part of the works that 11 explicitly refer to the subject in their title or abstract and are therefore easily accessible in the 12 SCOPUS and/orWeb of Science - Clarivate databases.