Normal Distribution, Maxwell Boltzmann, Brownian Motion, Diffusion Equation, Entropy.
n(v) ~ exp[-(1/2)βmv²], which can be written as the probability of finding a molecule whose velocity components are (v_x, v_y, v_z): f_v(v_x, v_y, v_z) = C³ exp[-(1/2)βm{(v_x)² +(v_y)²+(v_z)²}] Since the velocity components are independent (due to the orthogonality of the Cartesian coordinate),