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In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applications include many problems in the fields of physics, biology, [1] chemistry, neuroscience, [2] computer science, [3] [4] information theory [5] and ...
Statistical mechanics : an advanced course with problems and solutions / Ryogo Kubo, in cooperation with Hiroshi Ichimura, Tsunemaru Usui, Natsuki Hashitsume (1965, 7th edit.1988) Many-body theory : lectures / edited by Ryōgo Kubo (1966) Dynamical processes in solid state optics / edited by Ryōgo Kubo and Hiroshi Kamimura(1967)
Transfer-matrix methods have been critical for many exact solutions of problems in statistical mechanics, including the Zimm–Bragg and Lifson–Roig models of the helix-coil transition, transfer matrix models for protein-DNA binding, as well as the famous exact solution of the two-dimensional Ising model by Lars Onsager.
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 relativity, cosmology, and statistical mechanics. Videos for all of these courses are available online.
This category deals with exactly solvable models or integrable systems in physics, and specifically in statistical mechanics, quantum field theory and fluid mechanics.There are relatively few models in physics which have non-linear terms or couplings, and can still be solved exactly (that is, without resorting to perturbation theory); thus, such models are celebrated.
The random energy model (REM) is one of the simplest models of statistical mechanics of disordered systems, and probably the simplest model to show the meaning and power of the replica trick to the level 1 of replica symmetry breaking. The model is especially suitable for this introduction because an exact result by a different procedure is ...
In statistical mechanics and information theory, the Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of the velocity of a particle under the influence of drag forces and random forces, as in Brownian motion. The equation can be generalized to other observables as ...
The general motivation to use the Monte Carlo method in statistical physics is to evaluate a multivariable integral. The typical problem begins with a system for which the Hamiltonian is known, it is at a given temperature and it follows the Boltzmann statistics .