Abstract
The preceding two chapters helped us to set up the formalism of statistical mechanics. We introduced in Chap.2 the density operators \(\hat D\), and their classical limit, the densities in phase. They sum up our knowledge about the system and enable us to make predictions of a statistical nature about physical quantities, the expectation values of which we can calculate, starting from \(\hat D\). In Chap.3 we defined the statistical entropy (\(\hat D\)) which measures the random nature, or disorder, of a density operator. In those two chapters we assumed that the latter was given. However, in order actually to be able to calculate the properties of a system which has been prepared in some given way we must know how to assign to it a density operator representing the physical situation that we want to describe. This problem of the choice of \(\hat D\) will be solved in the present chapter for thermodynamic equilibrium states. In order to find the general form, the so-called Boltzmann-Gibbs distribution, of the density operators, or the densities in phase, describing these states, we shall use a postulate of a statistical nature which is similar to the criteria used in statistics to find the unbiased probability law for a set of random events. We introduce in this way a general prediction method (§4.1.3). This method leads us to represent a system in thermodynamic equilibrium by the most disordered macro-state compatible with the macroscopic data (§4.1).
“L’équilibre est la loi suprême et mystérieuse du grand Tout.”
V. Hugo, Post-scriptum de ma Vie
“En remontant chez moi pour y passer la soirée à travailler de mon mieux, je me disais que le monde n’est pas construit pour l’équilibre. Le monde est désordre. L’équilibre n’est pas la règle, c’est l’exception.”
G. Duhamel, Maîtres, 1937
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E.T. Jaynes, Phys.Rev. 106, 620 (1957), 108, 171 (1957); starting in 1979, the proceedings of an annual workshop on maximum entropy methods are being published (MIT Press, Reidel, Cambridge University Press, Kluwer).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Balian, R. (1991). The Boltzmann-Gibbs Distribution. In: From Microphysics to Macrophysics. Texts and Monographs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45475-5_5
Download citation
DOI: https://doi.org/10.1007/978-3-540-45475-5_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-21916-4
Online ISBN: 978-3-540-45475-5
eBook Packages: Springer Book Archive