Classical statistical mechanics is classical mechanics + uncertainty.
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The Wigner distribution ( WD ) was first proposed for corrections to classical statistical mechanics in 1932 by Eugene Wigner.
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This is called the partition function; it is the quantum mechanical version of the canonical partition function of classical statistical mechanics.
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But classical statistical mechanics did not account for all of the properties of liquids and solids, nor of gases at low temperature.
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This can be used to explain many results from classical statistical mechanics, including the irreversibility of time and the increase of entropy.
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When combined with thermodynamics, classical mechanics leads to the Gibbs paradox of classical statistical mechanics, in which entropy is not a well-defined quantity . quanta.
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Each contributes an energy proportional to the square of its amplitude; therefore, according to classical statistical mechanics, equipartition holds, and the mean energy of each mode will be kT / 2.
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With professor Robert Herman, he also developed the basis of the two fluid model, a traffic model in traffic engineering for urban networks, analogous to the two fluid model in classical statistical mechanics.
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Both are essentially the same, except that the classical thermodynamic ideal gas is based on classical statistical mechanics, and certain thermodynamic parameters such as the entropy are only specified to within an undetermined additive constant.
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In classical statistical mechanics, the ensemble is a probability distribution over phase points ( as opposed to a single phase point in ordinary mechanics ), usually represented as a distribution in a phase space with canonical coordinates.
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