Boltzmann Average
- Page ID
- 1873
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The Boltzmann average (sometimes known as the thermal average) for a given quantity or observable, let us say A, is given by
\[ \langle A \rangle= \frac{\sum_{i}Ae^{-E_i/k_BT}}{\sum_{i}e^{^{-E_{i}/k_BT}}} \nonumber\]
where kB is the Boltzmann constant, and T is the temperature. This provides the expected value of the property in question at a given temperature. This equation assumes non-degenerate states.
- Boltzmann Distribution
- 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.
- The Boltzmann constant
- The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. It is named after the Austrian physicist Ludwig Eduard Boltzmann.