Abstract
In this chapter we examine the surprising consequences of maximizing the Boltzmann-Gibbs entropy subject to various constraints. In Section A we show that for a system operating in a phase space of finite measure with no other constraints, the entropy will assume a maximal value if and only if the density (in the terminology of Gibbs) is the density of the microcanonical ensemble. Further, in Section B for a general phase space it is demonstrated that given the expectation value of a particular observable, the Boltzmann-Gibbs entropy of a density will attain its maximum if and only if the density is a generalization of the density of the canonical ensemble.
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© 1992 Springer Science+Business Media New York
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Mackey, M.C. (1992). Maximal Entropy Principles. In: Time’s Arrow: The Origins of Thermodynamic Behavior. Springer Study Edition. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9524-9_2
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DOI: https://doi.org/10.1007/978-1-4613-9524-9_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94093-9
Online ISBN: 978-1-4613-9524-9
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