Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2001-09-18
p. 331 in "Bayesian Inference and Maximum Entropy Methods in Science and Engineering" ed. by R. L. Fry (A.I.P. Vol. 617, 2002)
Physics
Condensed Matter
Statistical Mechanics
Presented at MaxEnt 2001, the 21th International Workshop on Bayesian Inference and Maximum Entropy Methods (August 4-9, 2001,
Scientific paper
10.1063/1.1477057
The ``Gibbs Paradox'' refers to several related questions concerning entropy in thermodynamics and statistical mechanics: whether it is an extensive quantity or not, how it changes when identical particles are mixed, and the proper way to count states in systems of identical particles. Several authors have recognized that the paradox is resolved once it is realized that there is no such thing as the entropy of a system, that there are many entropies, and that the choice between treating particles as being distinguishable or not depends on the resolution of the experiment. The purpose of this note is essentially pedagogical; we add to their analysis by examining the paradox from the point of view of information theory. Our argument is based on that `grouping' property of entropy that Shannon recognized, by including it among his axioms, as an essential requirement on any measure of information. Not only does it provide the right connection between different entropies but, in addition, it draws our attention to the obvious fact that addressing issues of distinguishability and of counting states requires a clear idea about what precisely do we mean by a state.
Caticha Ariel
Tseng Chih-Yuan
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