Normal Distribution, Maxwell Boltzmann, Brownian Motion, Diffusion Equation, Entropy.
(11) gives N = exp(-α) Z (12), where Z = Σ exp(-β ε_i), which is called the partition function. Dividing (11) by (12) gives the Maxwell Boltzmann distribution as n_i = (N/Z)exp(-β ε_i). If a molecule with mass m has only kinetic energy, ε_i =(1/2)mv², then the number of molecules with velocity v is