@MISC{Irwin09physicsof, author = {Irwin and Joan Jacobs and Neri Merhav and Neri Merhav}, title = {Physics of the Shannon Limits}, year = {2009} }

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Abstract

Abstract—We provide a simple physical interpretation, in the context of the second law of thermodynamics, to the information inequality (a.k.a. the Gibbs ’ inequality, which is also equivalent to the log–sum inequality), asserting that the relative entropy between two probability distributions cannot be negative. Since this inequality stands at the basis of the data processing theorem (DPT), and the DPT in turn is at the heart of most, if not all, proofs of converse theorems in Shannon theory, it is observed that conceptually, the roots of fundamental limits of Information Theory can actually be attributed to the laws of physics, in particular, the second law of thermodynamics, and indirectely, also the law of energy conservation. By the same token, in the other direction: one can view the second law as stemming from information–theoretic principles. Index Terms—Gibbs ’ inequality, data processing theorem, entropy, second law of thermodynamics, divergence, relative entropy, mutual information. I.