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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.
At the same time, Gibbs fully generalized and expanded statistical mechanics into the form in which it is known today. Gibbs showed how statistical mechanics could be used even to extend thermodynamics beyond classical thermodynamics, to systems of any number of degrees of freedom (including microscopic systems) and non-extensive systems.
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).
In statistical mechanics, the cluster expansion (also called the high temperature expansion or hopping expansion) is a power series expansion of the partition function of a statistical field theory around a model that is a union of non-interacting 0-dimensional field theories.
The series commenced with What You Need to Know (above) reissued under the title Classical Mechanics: The Theoretical Minimum. The series presently stands at four books (as of early 2023) covering the first four of six core courses devoted to: classical mechanics , quantum mechanics , special relativity and classical field theory , general ...
The series includes the volumes Mechanics, Mechanics of Deformable Bodies, Electrodynamics, Optics, Thermodynamics and Statistical Mechanics, and Partial Differential Equations in Physics. Focusing on one subject each semester, the lectures formed a three-year cycle of courses that Sommerfeld repeatedly taught at the University of Munich for ...
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.