Log-normal distributions describe data from diverse disciplines of science. However, the fundamental basis of log-normal distributions is unknown. We suggest that the skewed distributions are outcomes of natural processes i.e. they result from the principle of increasing entropy. Fluctuations during the course of evolution toward more probable states yield multiplicative variations about the mean. The non-linear dispersion of thermodynamic states, i.e. matter and energy defined by chemical potentials, underlies the skew. Cumulative curves of skewed distributions without integrable analytical forms are characteristic of natural processes.