Microstate

Definition

Consider a physical system made of many components.

1. Take a classical system of $N$ point particles in $\R^d$. A microstate is a point $(q_1, \dots, q_N, p_1, \dots, p_N)$ of the phase space $\Gamma = \R^{dN} \times \R^{dN}$. Here $q_i$ is the position and $p_i$ the momentum of particle $i$.
2. Take a lattice model with a finite set $\Lambda$ of sites and a finite set $S$ of single-site values. A microstate is a configuration $\sigma \in S^\Lambda$.
3. Take a quantum system with Hilbert space $\mathcal{H}$. A microstate is a pure state, that is, a unit vector of $\mathcal{H}$ up to a phase. In counting arguments one uses the vectors of an orthonormal basis of energy eigenstates.

A macrostate is a set of microstates singled out by the values of a few macroscopic quantities. Typical such quantities are the energy $E$, the volume $V$ and the number $N$ of particles.