Order at one scale can be the statistical consequence of disorder at another.

The Boltzmann-Gibbs distribution describes how particles or systems spread themselves among available energy states when they are in thermal equilibrium. Lower-energy states are more likely, while higher-energy states become exponentially less probable according to the factor e^−E/kT. Temperature sets the scale: at low temperatures, systems crowd into low-energy states; as temperature rises, higher-energy possibilities become increasingly populated. This simple statistical rule connects microscopic randomness with macroscopic properties such as pressure, heat capacity, and chemical equilibrium. It is one of the bridges between probability and thermodynamics. It is used primarily in statistical mechanics, thermodynamics, and physical chemistry.