Foundations of entropy in complex systems (opens in new tab)

This chapter reviews the foundations of entropy and their extensions to complex systems. We first discuss the relation between Boltzmann's formula, multiplicity, coarse-graining, and Shannon entropy, before introducing generalized entropies such as R\'enyi, Tsallis, and Burg entropy. We then examine Maxwell--Boltzmann, Bose--Einstein, and Fermi--Dirac statistics, structure-forming systems, sample-space reducing processes, P\'olya urns, and nonli...