Statistical mechanics

Statistical mechanics is the application of statistics, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. It provides a framework for relating the microscopic properties of individual atoms and molecules to the macroscopic or bulk properties of materials that can be observed in every day life, therefore explaining thermodynamics as a natural result of statistics and mechanics (classical and quantum). In particular, it can be used to calculate the thermodynamic properties of bulk materials from the spectroscopic data of individual molecules.

Microcanonical ensemble

At the heart of statistical mechanics lies Boltzmann's definition of entropy of a physical system:

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::S=k_Bln left(Omega ight) ,

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:where

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:S is the system entropy,

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:k_B is the Boltzmann constant, which will be referred to as simply k for the remainder of the article,

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:Omega is the number of microstates corresponding to the macroscopic state.

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Because a microcanonical ensemble is composed of a large set of identically prepared, isolated systems, the total internal energy of each system in the ensemble is identical. Thus, the total number of microstates corresponding to the observed macroscopic state is equal to the degeneracy of the observed energy level.

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