  We derive an explicit mapping between the spectra of conserved local
operators of integrable quantum lattice models and the density distributions of
their thermodynamic particle content. This is presented explicitly for the
Heisenberg XXZ spin chain. As an application we discuss a quantum quench
scenario, in both the gapped and critical regimes. We outline an exact
technique which allows for an efficient implementation on periodic matrix
product states. In addition, for certain simple product states we obtain
analytic closed-form expressions in terms of solutions to Hirota functional
relations. Remarkably, no reference to a maximal entropy principle is invoked.
