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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 ...
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 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.
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 ...
The second part of the text presents the foundations of classical statistical mechanics. The concept of Boltzmann's entropy is introduced and used to describe the Einstein model, the two-state system, and the polymer model. Afterwards, the different statistical ensembles are discussed from which the thermodynamics potentials are derived.
In physics, Liouville's theorem, named after the French mathematician Joseph Liouville, is a key theorem in classical statistical and Hamiltonian mechanics.It asserts that the phase-space distribution function is constant along the trajectories of the system—that is that the density of system points in the vicinity of a given system point traveling through phase-space is constant with time.
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 the two academic years 1977–1978 and 1981–1982 he taught in Taiwan at Tsinghua University, where he wrote in Chinese an advanced text on statistical mechanics — the book, published in 1983, "eschews the traditional approach built on the Gibbs ensemble." World Scientific published an English translation in 1985. In 1986 World Scientific ...