On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law (opens in new tab)

Power-law (PL) distribution functions (DF) are prevalent in highly diverse systems. The systems range in size from nanometer to mega light years, in complexity from dust grains to living organisms, and characterize the distribution of various events in nature and in various human activities. To gain some insight on why PL DF are so prevalent, we explore the conditions leading to the formation of a PL DF in a simple system of colliding hard sph...