Normal Distribution, Maxwell Boltzmann, Brownian Motion, Diffusion Equation, Entropy.
by α and (8) by β (Lagrange multipliers for maximalisation with the above constraints) and then adding (6), (7) and (8) yields Σ δn_i [ln n_i + α + β ε_i] = 0 .…(9). To make (9) hold, we need ln n_i + α +β ε_i = 0 (10). Solving (10) for n_i, we obtain n_i = exp(-α) exp(-β ε_i) (11). Summing over