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Entropy, Volume 3, Issue 1 (March 2001), Pages 1-26

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Research

Open AccessArticle Some Observations on the Concepts of Information-Theoretic Entropy and Randomness
Entropy 2001, 3(1), 1-11; doi:10.3390/e3010001
Received: 15 February 2000 / Accepted: 11 January 2001 / Published: 1 February 2001
Cited by 9 | PDF Full-text (130 KB)
Abstract
Certain aspects of the history, derivation, and physical application of the information-theoretic entropy concept are discussed. Pre-dating Shannon, the concept is traced back to Pauli. A derivation from first principles is given, without use of approximations. The concept depends on the underlying degree
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Certain aspects of the history, derivation, and physical application of the information-theoretic entropy concept are discussed. Pre-dating Shannon, the concept is traced back to Pauli. A derivation from first principles is given, without use of approximations. The concept depends on the underlying degree of randomness. In physical applications, this translates to dependence on the experimental apparatus available. An example illustrates how this dependence affects Prigogine's proposal for the use of the Second Law of Thermodynamics as a selection principle for the breaking of time symmetry. The dependence also serves to yield a resolution of the so-called ``Gibbs Paradox.'' Extension of the concept from the discrete to the continuous case is discussed. The usual extension is shown to be dimensionally incorrect. Correction introduces a reference density, leading to the concept of Kullback entropy. Practical relativistic considerations suggest a possible proper reference density. Full article
(This article belongs to the Special Issue Gibbs Paradox and Its Resolutions)
Open AccessArticle An Elementary Derivation of The Black Hole Entropy in Any Dimension
Entropy 2001, 3(1), 12-26; doi:10.3390/e3010012
Received: 30 April 2000 / Accepted: 22 November 2000 / Published: 26 March 2001
Cited by 5 | PDF Full-text (154 KB)
Abstract
An elementary derivation of the Black Hole Entropy area relation in any dimension is provided based on the New Extended Scale Relativity Principle and Shannon's Information Entropy. The well known entropy-area linear Bekenstein-Hawking relation is derived. We discuss briefly how to derive the
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An elementary derivation of the Black Hole Entropy area relation in any dimension is provided based on the New Extended Scale Relativity Principle and Shannon's Information Entropy. The well known entropy-area linear Bekenstein-Hawking relation is derived. We discuss briefly how to derive the most recently obtained Logarithmic and higher order corrections to the linear entropy-area law in full agreement with the standard results in the literature. Full article
(This article belongs to the Special Issue Recent Advances in Entanglement and Quantum Information Theory)

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