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Elementary Principles in Statistical Mechanics, published in March 1902, is a work of scientific literature by Josiah Willard Gibbs which is considered to be the foundation of modern statistical mechanics. Its full title was Elementary Principles in Statistical Mechanics, developed with especial reference to the rational foundation of ...
In statistical mechanics, the hard hexagon model is a 2-dimensional lattice model of a gas, where particles are allowed to be on the vertices of a triangular lattice but no two particles may be adjacent. The model was solved by Baxter , who found that it was related to the Rogers–Ramanujan identities.
Introduction to Modern Statistical Mechanics. Oxford University Press. ISBN 0-19-504277-8. [78] [79] [80] W.A. Wassam, Jr. (2002). Statistical Mechanics : Encyclopedia of Physical Science and Technology, Third Edition, Volume 15. Academic Press. ISBN 978-0-12-227410-7. Bowley, Roger and Sanchez, Mariana (2000). Introductory Statistical ...
In statistical mechanics, the Kac ring is a toy model [1] introduced by Mark Kac in 1956 [2] [3] to explain how the second law of thermodynamics emerges from time-symmetric interactions between molecules (see reversibility paradox).
The Knudsen number is a dimensionless number defined as =, where = mean free path [L 1], = representative physical length scale [L 1].. The representative length scale considered, , may correspond to various physical traits of a system, but most commonly relates to a gap length over which thermal transport or mass transport occurs through a gas phase.
All classical statistical physics is based on the concentration of measure phenomena: The fundamental idea (‘theorem’) about equivalence of ensembles in thermodynamic limit (Gibbs, 1902 [4] and Einstein, 1902-1904 [5] [6] [7]) is exactly the thin shell concentration theorem.
In a crucial paper (1933), Dirac [7] explained how classical mechanics is an emergent phenomenon of quantum mechanics: destructive interference among paths with non-extremal macroscopic actions S » ħ obliterate amplitude contributions in the path integral he introduced, leaving the extremal action S class, thus the classical action path as ...
In statistical mechanics, Maxwell–Boltzmann statistics describes the distribution of classical material particles over various energy states in thermal equilibrium. It is applicable when the temperature is high enough or the particle density is low enough to render quantum effects negligible.