Common origin of power-law tails in income distributions and relativistic gases

• Power-law tails, or “fat tails”, occur frequently in income distributions and energy distributions of relativistic gases.
• They require a protection mechanism allowing individuals/particles to preserve their wealth/energy in the interactions.
• This can be proven through wealth exchange models in economics, and through kinematical laws in physics.
• Thus in both fields a certain feature of the microscopic interactions leads to the same macroscopic consequences.

Power-law tails are ubiquitous in income distributions and in the energy distributions of diluted relativistic gases. We analyze the conceptual link between these two cases. In economic interactions fat tails arise because the richest individuals enact some protection mechanisms (“saving propensity”) which allow them to put at stake, in their interactions, only a small part of their wealth. In high-energy particle collisions something similar happens, in the sense that when particles with very large energy collide with slow particles, then as a sole consequence of relativistic kinematics (mass dilation), they tend to exchange only a small part of their energy; processes like the frontal collision of two identical particles, where the exchanged energy is 100%, are very improbable, at least in a diluted gas. We thus show how in two completely different systems, one of socio-economic nature and one of physical nature, a certain feature of the binary microscopic interactions leads to the same consequence in the macroscopic distribution for the income or respectively for the energy.