DISTRIBUTION FUNCTION

mathematical expression that describes the probability that a system will take on a specific value or set of values. For example, the probability (dP) that a molecule of gas will be found with velocity components u, v, and w in the x, y, and z directions, respectively, is given by the product of the distribution function and the infinitesimal volume du dv dw; i.e., dP = f (u, v, w) du dv dw, in which f (u, v, w) is the distribution function describing the velocity of the molecule and dP is the probability of finding the x component of velocity between u and u + du, the y component between v and v + dv, etc. (see MaxwellBoltzmann distribution law). A complete description of a system may involve other variables as well, such as position and orientation. Distribution functions may take into account any or all such variables.