Equilibrium ensembles (those that do not evolve over time, d ρ ρ ^ ^ / d t = 0 ) can be written solely as a function of conserved variables. For example, the microcanonical ensemble and canonical ensemble are strictly functions of the total energy, which is measured by the total energy operator H ^ ^ (Hamiltonian). The grand canonical ensemble is additionally a function of the particle number, measured by the total particle number operator N ^ ^ . Such equilibrium ensembles are a diagonal matrix in the orthogonal basis of states that simultaneously diagonalize each conserved variable. In bra–ket notation, the density matrix is