Statistical mechanics is the application of statistics to the field of mechanics. It relates the microscopic properties of individual atoms and molecules to the macroscopic or bulk properties of materials, hence explaining thermodynamics as a natural result of statistics and (classical or quantum) mechanics. It can, for example, predict the thermodynamic properties of bulk materials from the spectroscopic data of individual molecules.
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This category includes the aspects of statistical mechanics that are derived from the use of quantum mechanical concepts, such as Fermi-Dirac statistics.