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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 ...
In statistical thermodynamics, UNIQUAC (a portmanteau of universal quasichemical) is an activity coefficient model used in description of phase equilibria. [ 1 ] [ 2 ] The model is a so-called lattice model and has been derived from a first order approximation of interacting molecule surfaces.
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 ...
Three important thermodynamic ensembles were defined by Gibbs: [2] Microcanonical ensemble (or NVE ensemble) —a statistical ensemble where the total energy of the system and the number of particles in the system are each fixed to particular values; each of the members of the ensemble are required to have the same total energy and particle ...
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.
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).
Despite the foregoing, there is a difference between the two quantities. The information entropy Η can be calculated for any probability distribution (if the "message" is taken to be that the event i which had probability p i occurred, out of the space of the events possible), while the thermodynamic entropy S refers to thermodynamic probabilities p i specifically.