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Maximal Entropy Principles

  • Michael C. Mackey
Part of the Springer Study Edition book series (SSE)

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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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Michael C. Mackey
    • 1
  1. 1.Center for Nonlinear Dynamics in Physiology and MedicineMcGill UniversityMontrealCanada

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