An instructive model of entropy

This article first notes the misinterpretation of a common thought experiment, and the misleading comment that 'systems tend to flow from less probable to more probable macrostates'. It analyses the experiment, generalizes it and introduces a new tool of investigation, the simplectic struc...

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Bibliographic Details
Published inInternational journal of mathematical education in science and technology Vol. 41; no. 6; pp. 805 - 818
Main Author Zimmerman, Seth
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.01.2010
Taylor & Francis, Ltd
Subjects
combinatorial model
Concept Teaching
information entropy
Mathematical Formulas
Mathematical Logic
Misconceptions
missing information
multinomials
Physics
Science Experiments
Scientific Concepts
Scientific Methodology
Scientific Principles
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ISSN0020-739X
1464-5211
DOI10.1080/0020739X.2010.486447

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Summary:This article first notes the misinterpretation of a common thought experiment, and the misleading comment that 'systems tend to flow from less probable to more probable macrostates'. It analyses the experiment, generalizes it and introduces a new tool of investigation, the simplectic structure. A time-symmetric model is built upon this structure, yielding several non-intuitive results. The approach is combinatorial rather than statistical, and assumes that entropy is equivalent to 'missing information'. The intention of this article is not only to present interesting results, but also, by deliberately starting with a simple example and developing it through proof and computer simulation, to clarify the often confusing subject of entropy. The article should be particularly stimulating to students and instructors of discrete mathematics or undergraduate physics.
ISSN:0020-739X
1464-5211
DOI:10.1080/0020739X.2010.486447