  For each \(x\), henceforth also called the microstate, we define the macrostate (Boltzmann's term was Komplexion) as \(Z := (n_1,\ldots,n_m)\), where \(n_i\) is the number of particles that have their molecular state in cell \(\omega_i\). The relation between macro- and microstate is obviously non-unique since many different microstates, e.g., obtained by permuting the molecules, lead to the same macrostate.  One may associate with every given macrostate \(Z_0\) the corresponding set of microstates: