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The maximum-term method is a consequence of the large numbers encountered in statistical mechanics.It states that under appropriate conditions the logarithm of a summation is essentially equal to the logarithm of the maximum term in the summation.
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 ...
Thermodynamic formalism : the mathematical structures of classical equilibrium statistical mechanics. Addison-Wesley. ISBN 0-201-13504-3.; (1984) Cambridge: University Press ISBN 0-521-30225-0. 2e (2004) Cambridge: University Press ISBN 0-521-54649-4 [88] [89] Minlos, Robert Adol'fovich (2000). Introduction to Mathematical Statistical Mechanics ...
Using statistical mechanics, the KB theory derives thermodynamic quantities from pair correlation functions between all molecules in a multi-component solution. [1] The KB theory proves to be a valuable tool for validation of molecular simulations, as well as for the molecular-resolution elucidation of the mechanisms underlying various physical ...
In statistical mechanics and thermodynamics the compressibility equation refers to an equation which relates the isothermal compressibility (and indirectly the pressure) to the structure of the liquid.
With a model of the microscopic constituents of a system, one can calculate the microstate energies, and thus the partition function, which will then allow us to calculate all the other thermodynamic properties of the system. The partition function can be related to thermodynamic properties because it has a very important statistical meaning.
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This is known as the Gibbs algorithm, having been introduced by J. Willard Gibbs in 1878, to set up statistical ensembles to predict the properties of thermodynamic systems at equilibrium. It is the cornerstone of the statistical mechanical analysis of the thermodynamic properties of equilibrium systems (see partition function).