An information measure that leads to a power-law distribution

Abstract

Information measures are important in physics since they describe the behavior of physical systems. Besides the famous Shannon entopy, there are many information measure that describes complex sytems common in nature. In this paper, the infomation measure used is in the form I = Σ p_i^(1+1/ν) where ν = 1, 2, 3, · · ·. The statistical mechanics derived from this measure leads to a system that describes a power-law distribution. A physical model of hydrogen atoms was also formulated which can be described by the derived distribution.