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General derivations of the equipartition theorem can be found in many statistical mechanics textbooks, both for the microcanonical ensemble and for the canonical ensemble.
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In many statistical and mechanic models, an END assumption among the random variables in the models is more reasonable than an independent or NA assumption.
Mean-field approaches have applications in many areas such as statistical mechanics and physics, quantum mechanics and quantum chemistry.
This review also covers many fundamental aspects of statistical mechanics, such as the derivation of variational principles characterizing equilibrium and nonequilibrium states, the breaking of the Legendre transform for nonconcave entropies, and the characterization of nonequilibrium fluctuations through fluctuation relations.
Many notions of classical statistical mechanics such as probability distributions and mean values are retained in this picture, which recovers physical intuition in the field of quantum theory.
As such, statistical mechanics has many practical applications in glass science and technology.
The second part goes through many problems and results of statistical mechanics, and shows how these can be formulated and derived within the context of large deviation theory.
As even a cursory glance at statistical mechanics reveals, there are many candidates for the statistical mechanical entropy, each the center of a different program in the foundations of the field.
Many of the philosophical issues in statistical mechanics center around the notion of probability as it appears in the theory.
Many authors use the tool of statistical mechanics to describe the deformation behaviour of the entire network.
The ASCLT has already received applications in many fields, including condensed matter physics, statistical mechanics, ergodic theory and dynamical systems, and control and information and quanitle estimation.
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