Editing Partition function
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The '''partition function''' | The '''partition function''' of a system in contact with a thermal bath | ||
at temperature <math>T</math> is the normalization constant of the [[Boltzmann distribution]] | at temperature <math>T</math> is the normalization constant of the [[Boltzmann distribution]] | ||
function, and therefore its expression is given by | function, and therefore its expression is given by | ||
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where <math>\Omega(E)</math> is the [[density of states]] with energy <math>E</math> and <math>k_B</math> | where <math>\Omega(E)</math> is the [[density of states]] with energy <math>E</math> and <math>k_B</math> | ||
the [[Boltzmann constant]] | the [[Boltzmann constant]]. | ||
The partition function of a system is related to the [[Helmholtz energy function]] through the formula | The partition function of a system is related to the [[Helmholtz energy function]] through the formula | ||
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This connection can be derived from the fact that <math>k_B\log\Omega(E)</math> is the | This connection can be derived from the fact that <math>k_B\log\Omega(E)</math> is the | ||
[[entropy]] of a system with total energy <math>E</math>. This is an [[ | [[entropy]] of a system with total energy <math>E</math>. This is an [[extensive magnitude]] in the | ||
sense that, for large systems (i.e. in the [[thermodynamic limit]], when the number of | sense that, for large systems (i.e. in the [[thermodynamic limit]], when the number of | ||
particles <math>N\to\infty</math> | particles <math>N\to\infty</math> | ||
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These equations provide a link between [[Classical thermodynamics | classical thermodynamics]] and | These equations provide a link between [[Classical thermodynamics | classical thermodynamics]] and | ||
[[Statistical mechanics | statistical mechanics]] | [[Statistical mechanics | statistical mechanics]] | ||
[[category:classical thermodynamics]] | [[category:classical thermodynamics]] | ||
[[category:statistical mechanics]] | [[category:statistical mechanics]] |