macrostate

A macrostate is a set of macroscopic properties that describe a physical system, specified by variables such as temperature, pressure, volume, energy, particle number, magnetization, and composition. It captures the large-scale behavior without detailing the exact microscopic configuration. A single macrostate can be realized by many different microscopic configurations, or microstates, that are consistent with the same macroscopic description.

The multiplicity Ω of a macrostate is the number of microstates corresponding to it. In statistical mechanics, entropy S is related to Ω by S = k_B ln Ω, where k_B is Boltzmann’s constant. Therefore, macrostates with higher multiplicity have higher entropy and are statistically more probable at equilibrium.

In a system with fixed energy, volume, and particle number, the equilibrium macrostate is the one with the largest Ω. Real systems exhibit fluctuations: microstates within a macrostate continuously change, and, in finite systems, the system may transition between macrostates, though such transitions become less likely as entropy differences grow.

Practical examples include a gas in a container, where the macrostate is defined by energy, volume, and particle number, while microstates specify the exact positions and momenta of all molecules. In lattice models, macrostate variables might be the total magnetization or density. Coarse-graining is the process of grouping microstates into macrostates by ignoring fine details, a foundational idea behind thermodynamics and statistical ensembles (such as microcanonical, canonical, and grand canonical ensembles) that relate microscopic behavior to macroscopic observables.