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 $$ \mathrm{J} $$ Energy of a gas particle
Chemical potential
$$ \mu $$ Unit $$ \mathrm{J} $$ Chemical potential indicates the change in internal energy when the number of particles of the classical gas changes.
Temperature
$$ T $$ Unit $$ \mathrm{K} $$ Absolute temperature of the gas.
Boltzmann Constant
$$ k_{\text B} $$ Unit $$ \frac{\mathrm J}{\mathrm K} = \frac{\mathrm{kg} \,\mathrm{m}^2}{\mathrm{s}^2 \, \mathrm{K}} $$ Boltzmann constant is a physical constant from many-particle physics and has the following exact value:$$ k_{\text B} ~=~ 1.380 \, 649 ~\cdot~ 10^{-23} \, \frac{\mathrm{J}}{\mathrm{K}} $$