カノニカル分布 (Canonical ensemble)

ボルツマン分布 (Boltzmann distribution)

P(Ei)=1Zexp(−βEi) P \left( E_i \right) = \frac{1}{Z} \exp \left( -\beta E_i \right)

where $\beta $ is given by

β=1kBT \beta = \frac{1}{k_B T}

$Z$ is the Partition Function, $k_B$ is Boltzmann's Constant, $T$ is temperature and $E_i$ is the energy of state $i$.

ボルツマン定数 (Boltzmann constant)

kB=RNA=1.3806504(24)×1023[J/K] k_B = \frac{R}{N_A} = 1.3806504(24) \times 10^23 [J/K]

$R$ is the gas constant, $N_A$ is the Avogadro constant.

分配関数 (Partition function)

Z=∑ie−βEi Z = \sum_i e^{-\beta E_i}