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ISSN: 2161-0398

Journal of Physical Chemistry & Biophysics
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Research Article

Comments on the Extensivity of the Boltzmann Entropy

Roland Riek* and Alexander Sobol
Laboratory of Physical Chemistry, ETH Zurich, Switzerland
*Corresponding Author : Roland Riek
Laboratory of Physical Chemistry
ETH Zurich, Switzerland
E-mail: [email protected]
Received: February 12, 2016 Accepted: March 02, 2016 Published: March 07, 2016
Citation: Riek R, Sobol A (2016) Comments on the Extensivity of the Boltzmann Entropy. J Phys Chem Biophys 6:207. doi:10.4172/2161-0398.1000207
Copyright: © 2016 Riek R, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Abstract

In thermodynamics entropy Std is an extensive state function. Its derivation by statistical mechanics following Boltzmann and Gibbs with the famous formula S=kBlnW for a micro-canonical ensemble with N particles, kB the Boltzmann constant, and W the number of accessible micro-states is however in general not extensive unless the Stirling approximation given by lnN! – NlnN + N is used. Furthermore, at the thermodynamic limit with the number of particles N→∞ at constant density the Stirling approximation can not be used to show extensivity because limN→∞ (lnN! – NlnN + N)=∞. Hence, the Boltzmann entropy S as shown here for the ideal gas is neither for a small system with N particles nor at the thermodynamic limit extensive. Thus, if strict extensivity for the entropy is requested the claim of statistical mechanics that the Boltzmann entropy is a microscopic description of its thermodynamic analog is challenged.

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