Microstate (classical)

A microstate of a classical mechanical system is a complete specification of its instantaneous configuration: the positions and momenta of all constituent particles.

Formally, a microstate is a point $(q, p)$ in the system’s phase space $\Gamma$.

Contrast with macrostate

While a microstate specifies all microscopic details, a macrostate specifies only macroscopic observables (temperature, pressure, volume, etc.). Many distinct microstates typically correspond to the same macrostate.

In statistical mechanics

The fundamental postulate of statistical mechanics is that equilibrium properties can be computed by averaging over microstates according to an appropriate probability distribution:

• Microcanonical ensemble : uniform distribution over microstates at fixed energy.
• Canonical ensemble : Boltzmann distribution $\propto e^{-\beta H}$ over all microstates.
• Grand canonical ensemble : distribution over microstates with varying particle number.