Formula Boltzmann distribution function Probability Energy Chemical potential Temperature
$$P(W) ~=~ \mathrm{e}^{ -\frac{ W - \mu }{ k_{\text B} \, T}}$$ $$P(W) ~=~ \mathrm{e}^{ -\frac{ W - \mu }{ k_{\text B} \, T}}$$ $$W ~=~ - \ln(P(W)) \, k_{\text B} \, T - \mu$$ $$\mu ~=~ - \ln(P(W)) \, k_{\text B} \, T - W$$ $$T ~=~ \frac{-W-\mu}{ \ln(P(W)) \, k_{\text B} }$$
Probability
\( P(W) \) Unit \( - \) The occupation probability indicates with which probability \(P\) a state with energy \( W \) at temperature \( T \) is occupied by a particle (for example high temperature electron gas).
Energy
\( W \) Unit \( \text{J} \) Energy of a gas particle
Chemical potential
\( \mu \) Unit \( \text{J} \) Chemical potential indicates the change in internal energy when the number of particles of the classical gas changes.
Temperature
\( T \) Unit \( \text{K} \) Absolute temperature of the gas.
Boltzmann constant
\( k_{\text B} \) Unit \( \frac{\text J}{\text K} \) Boltzmann constant is a natural constant, which is used more often in statistical physics and thermodynamics. It has the value: \( k_{\text B} = 1.380 \, 649 \, \cdot\, 10^{-23} \, \frac{\text J}{\text K} \).