§ DICTIONARY · CONCEPT

Macrostate

The coarse, measurable description of a system — pressure, volume, temperature, particle number — shared by enormously many microstates.

§ 01

Definition

A macrostate is the description of a system in terms of the few quantities a laboratory can actually measure: pressure P, volume V, temperature T, and particle number N, together with totals like energy. A handful of numbers stands in for the 10²⁴ that specify a microstate. Crucially, a single macrostate is realised by an immense family of microstates — every microscopic configuration consistent with those measured values.

The number of microstates belonging to a macrostate is its multiplicity, Ω. Macrostates differ wildly in multiplicity: an 'all molecules in the left half' macrostate has vastly fewer microstates than a 'molecules spread evenly' one. Because the fundamental postulate makes every microstate equally probable, a system is found, overwhelmingly, in the macrostate of greatest multiplicity — which is what equilibrium is.

Thermodynamics is the science of macrostates and the transitions between them; statistical mechanics explains those macrostates as the most probable outcomes of counting microstates.

§ 02

History

The notion was made precise by Boltzmann's connection between entropy and microstate counting (1877) and generalised by Gibbs into the ensemble formalism around 1902.