ERIC Number: EJ818205
Record Type: Journal
Publication Date: 2008-May
Abstractor: As Provided
Reference Count: 10
A Formal Derivation of the Gibbs Entropy for Classical Systems Following the Schrodinger Quantum Mechanical Approach
Santillan, M.; Zeron, E. S.; Del Rio-Correa, J. L.
European Journal of Physics, v29 n3 p629-638 May 2008
In the traditional statistical mechanics textbooks, the entropy concept is first introduced for the microcanonical ensemble and then extended to the canonical and grand-canonical cases. However, in the authors' experience, this procedure makes it difficult for the student to see the bigger picture and, although quite ingenuous, the subtleness of the demonstrations to pass from the microcanonical to the canonical and grand-canonical ensembles is hard to grasp. In the present work, we adapt the approach used by Schrodinger to introduce the entropy definition for quantum mechanical systems to derive a classical mechanical entropy definition, which is valid for all ensembles and is in complete agreement with the Gibbs entropy. Afterwards, we show how the specific probability densities for the microcanonical and canonical ensembles can be obtained from the system macrostate, the entropy definition and the second law of thermodynamics. After teaching the approach introduced in this paper for several years, we have found that it allows a better understanding of the statistical mechanics foundations. On the other hand, since it demands previous knowledge of thermodynamics and mathematical analysis, in our experience this approach is more adequate for final-year undergraduate and graduate physics students.
Descriptors: Textbooks, Thermodynamics, Mechanics (Physics), Scientific Concepts, Probability, Quantum Mechanics, College Science, Science Instruction, Undergraduate Study, Graduate Study, Equations (Mathematics)
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Publication Type: Journal Articles; Reports - Research
Education Level: Higher Education
Authoring Institution: N/A