Page "Power law" Paragraph 5

The equivalence of power laws with a particular scaling exponent can have a deeper origin in the dynamical processes that generate the power-law relation.

In physics, for example, phase transitions in thermodynamic systems are associated with the emergence of power-law distributions of certain quantities, whose exponents are referred to as the critical exponents of the system.

Diverse systems with the same critical exponents — that is, which display identical scaling behaviour as they approach criticality — can be shown, via renormalization group theory, to share the same fundamental dynamics.

For instance, the behavior of water and CO < sub > 2 </ sub > at their boiling points fall in the same universality class because they have identical critical exponents.

In fact, almost all material phase transitions are described by a small set of universality classes.

Similar observations have been made, though not as comprehensively, for various self-organized critical systems, where the critical point of the system is an attractor.

Formally, this sharing of dynamics is referred to as universality, and systems with precisely the same critical exponents are said to belong to the same universality class.