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Entropy 2014, 16(6), 2990-3008; doi:10.3390/e16062990

Constraints of Compound Systems: Prerequisites for Thermodynamic Modeling Based on Shannon Entropy

Institute of Chemical Engineering and Environmental Technology, Graz University of Technology, NAWI Graz, Inffeldgasse 25/C/I, 8010 Graz, Austria
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Received: 14 April 2014 / Revised: 17 May 2014 / Accepted: 21 May 2014 / Published: 26 May 2014
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Abstract

Thermodynamic modeling of extensive systems usually implicitly assumes the additivity of entropy. Furthermore, if this modeling is based on the concept of Shannon entropy, additivity of the latter function must also be guaranteed. In this case, the constituents of a thermodynamic system are treated as subsystems of a compound system, and the Shannon entropy of the compound system must be subjected to constrained maximization. The scope of this paper is to clarify prerequisites for applying the concept of Shannon entropy and the maximum entropy principle to thermodynamic modeling of extensive systems. This is accomplished by investigating how the constraints of the compound system have to depend on mean values of the subsystems in order to ensure additivity. Two examples illustrate the basic ideas behind this approach, comprising the ideal gas model and condensed phase lattice systems as limiting cases of fluid phases. The paper is the first step towards developing a new approach for modeling interacting systems using the concept of Shannon entropy.
Keywords: Shannon entropy; constrained extremalization; compound systems; additivity; thermodynamic modeling; discrete states; discrete modeling Shannon entropy; constrained extremalization; compound systems; additivity; thermodynamic modeling; discrete states; discrete modeling
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Pfleger, M.; Wallek, T.; Pfennig, A. Constraints of Compound Systems: Prerequisites for Thermodynamic Modeling Based on Shannon Entropy. Entropy 2014, 16, 2990-3008.

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