“…Fluctuation theory [21,22,26, offers various notions to understand statistical and quantum properties of an ensemble of observations and instrumental technology towards a high precision measurement. À priori, we have investigated the above perspectives in the light of configurations emerging from condensed matter systems, e.g., [22,45,64], electrical engineering [50,51], computer science and engineering [52], and various high energy configurations such as the flat information geometries [48,53] and counting entropy [54] that it arises as a fluctuation theory of counting systems whose degeneracy is described as a selection problem. Hereby, we have examined statistical correlations and instabilities undermining the combinatorics of selecting n boxes out m = N 2 boxes, where n ≤ m. Further, we have extended studies of fluctuations for the configurations whose embedding function are defined by the Shannon entropy, Rènyi entropy, Tsallis entropy [46,47] and other higher order corrected entropies in the large charge limit of observations [48,49].…”