Entropy, Shannon’s Measure of Information and Boltzmann’s H-Theorem

Entropy, Shannon’s Measure of Information and Boltzmann’s H-Theorem

We start with a clear distinction between Shannon’s Measure of Information (SMI) and the Thermodynamic Entropy. The first is defined on any probability distribution; and therefore it is a very general concept. On the other hand Entropy is defined on a very special set of distributions. Next we show...

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Main Author: Arieh Ben-Naim
Format: Article
Language:English
Published: MDPI AG 2017-01-01
Series:Entropy
Subjects:
entropy
Shannon’s measure of information
Second Law of Thermodynamics
H-theorem
Online Access:http://www.mdpi.com/1099-4300/19/2/48
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spelling doaj-5c1eb22b3a4741ca8130d7d41df6a3bd2020-11-24T21:46:34ZengMDPI AGEntropy1099-43002017-01-011924810.3390/e19020048e19020048Entropy, Shannon’s Measure of Information and Boltzmann’s H-TheoremArieh Ben-Naim0Department of Physical Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, IsraelWe start with a clear distinction between Shannon’s Measure of Information (SMI) and the Thermodynamic Entropy. The first is defined on any probability distribution; and therefore it is a very general concept. On the other hand Entropy is defined on a very special set of distributions. Next we show that the Shannon Measure of Information (SMI) provides a solid and quantitative basis for the interpretation of the thermodynamic entropy. The entropy measures the uncertainty in the distribution of the locations and momenta of all the particles; as well as two corrections due to the uncertainty principle and the indistinguishability of the particles. Finally we show that the H-function as defined by Boltzmann is an SMI but not entropy. Therefore; much of what has been written on the H-theorem is irrelevant to entropy and the Second Law of Thermodynamics.http://www.mdpi.com/1099-4300/19/2/48entropyShannon’s measure of informationSecond Law of ThermodynamicsH-theorem
collection DOAJ
language English
format Article
sources DOAJ
author Arieh Ben-Naim
spellingShingle Arieh Ben-Naim
Entropy, Shannon’s Measure of Information and Boltzmann’s H-Theorem
Entropy
entropy
Shannon’s measure of information
Second Law of Thermodynamics
H-theorem
author_facet Arieh Ben-Naim
author_sort Arieh Ben-Naim
title Entropy, Shannon’s Measure of Information and Boltzmann’s H-Theorem
title_short Entropy, Shannon’s Measure of Information and Boltzmann’s H-Theorem
title_full Entropy, Shannon’s Measure of Information and Boltzmann’s H-Theorem
title_fullStr Entropy, Shannon’s Measure of Information and Boltzmann’s H-Theorem
title_full_unstemmed Entropy, Shannon’s Measure of Information and Boltzmann’s H-Theorem
title_sort entropy, shannon’s measure of information and boltzmann’s h-theorem
publisher MDPI AG
series Entropy
issn 1099-4300
publishDate 2017-01-01
description We start with a clear distinction between Shannon’s Measure of Information (SMI) and the Thermodynamic Entropy. The first is defined on any probability distribution; and therefore it is a very general concept. On the other hand Entropy is defined on a very special set of distributions. Next we show that the Shannon Measure of Information (SMI) provides a solid and quantitative basis for the interpretation of the thermodynamic entropy. The entropy measures the uncertainty in the distribution of the locations and momenta of all the particles; as well as two corrections due to the uncertainty principle and the indistinguishability of the particles. Finally we show that the H-function as defined by Boltzmann is an SMI but not entropy. Therefore; much of what has been written on the H-theorem is irrelevant to entropy and the Second Law of Thermodynamics.
topic entropy
Shannon’s measure of information
Second Law of Thermodynamics
H-theorem
url http://www.mdpi.com/1099-4300/19/2/48
work_keys_str_mv AT ariehbennaim entropyshannonsmeasureofinformationandboltzmannshtheorem
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