  The occurrence of the nonzero leftmost digit, i.e., 1, 2, ..., 9, of numbers
from many real world sources is not uniformly distributed as one might naively
expect, but instead, the nature favors smaller ones according to a logarithmic
distribution, named Benford's law. We investigate three kinds of widely used
physical statistics, i.e., the Boltzmann-Gibbs (BG) distribution, the
Fermi-Dirac (FD) distribution, and the Bose-Einstein (BE) distribution, and
find that the BG and FD distributions both fluctuate slightly in a periodic
manner around the Benford distribution with respect to the temperature of the
system, while the BE distribution conforms to it exactly whatever the
temperature is. Thus the Benford's law seems to present a general pattern for
physical statistics and might be even more fundamental and profound in nature.
Furthermore, various elegant properties of Benford's law, especially the
mantissa distribution of data sets, are discussed.
