Boltzmann distribution
= Boltzmann distribution
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{title2=$P_i=Z^{-1}e^{-\beta E_i}$}
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At thermal equilibrium, the Boltzmann distribution assigns a state of energy $E_i$ probability $P_i=Z^{-1}e^{-\beta E_i}$, where $\beta=(k_BT)^{-1}$ and the partition function $Z$ normalizes the probabilities.