A review for the entropic central limit theorem

In this paper, we review the research on the entropic central limit 定理 starting from the 1950s, including the analysis of the limit distribution of the sum of independent identically distributed random variables using the entropy method, the Berry-Esseen type bound for the entropic central limit 定理 and the convergence results in the non-independent case. By investigating the development of the entropic central limit 定理, we hope to exhibit the subtle relationship among thermodynamics, information theory, and probability theory. In the last part of this paper, we briefly introduce the latest research results of the authors about the entropic conditional central limit 定理 and its application to Hadamard compression.