Carlen, E. A.; Soffer, A. Entropy production by block variable summation and central limit theorems. (English) Zbl 0734.60024 Commun. Math. Phys. 140, No. 2, 339-371 (1991). Summary: We prove a strict lower bound on the entropy produced when independent random variables are summed and rescaled. Using this, we develop an approach to central limit theorems from a dynamical point of view in which the entropy is a Lyapunov functional governing approach to the Gaussian limit. This dynamical approach naturally extends to cover dependent variables, and leads to new results in pure probability theory as well as in statistical mechanics. It also provides a unified framework within which many previous results are easily derived. Cited in 28 Documents MSC: 60F05 Central limit and other weak theorems 82C35 Irreversible thermodynamics, including Onsager-Machlup theory Keywords:entropy; central limit theorems; Lyapunov functional PDFBibTeX XMLCite \textit{E. A. Carlen} and \textit{A. 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