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Boltzmann Distribution

  • Page ID
    1874
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    The Maxwell-Boltzmann distribution function is a function f(E) which gives the probability that a system in contact with a thermal bath at temperature T has energy E. This distribution is classical and is used to describe systems with identical but distinguishable particles.

    \[f(E) \propto \Omega(E) \exp \left[ - E/k_B T \right] \]

    where \(\Omega(E)\) is the degeneracy of the energy E; leading to

    \[f(E) = \frac{1}{Z} \Omega(E) \exp \left[ -E/k_B T \right] \]

    where

    • \(k_B\) is the Boltzmann constant,
    • \(T\) is the temperature, and
    • the normalization constant \(Z\) is the partition function of the system.

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