Entropy 2021 Best Paper Award.

The maximal positive I I i I k i identifies the variables that co-vary the most in the population, whereas the minimal negative I I i I k i identifies synergistic clusters and the variables that differentiate-segregate the most in the population. Detailed state variables are reduced using the usual principle of maximum entropy (MaxEnt), whereas relaxation of the conjugate variables guarantees that the reduced equations are closed. Pursuing the work of Hu Kuo Ting and Te Sun Han, we show that information functions provide coordinates for binary variables and that they are analytically independent of the probability simplex for any set of finite variables. [Extracted from the article]