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Entropy production by block variable summation and central limit theorems

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Princeton University, 08544, Princeton, NJ, USA

    E. A. Carlen & A. Soffer

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  1. E. A. Carlen
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  2. A. Soffer
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Additional information

Communicated by M. Aizenman

Partially supported by an NSF postdoctoral fellowship

Partially supported by NSF grant DMS-8905772; A. P. Sloan Fellow in Mathematics

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Carlen, E.A., Soffer, A. Entropy production by block variable summation and central limit theorems. Commun.Math. Phys. 140, 339–371 (1991). https://doi.org/10.1007/BF02099503

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