  In classical thermodynamics the Euler relation is an expression for the
internal energy as a sum of the products of canonical pairs of extensive and
intensive variables. For quantum systems the situation is more intricate, since
one has to account for the effects of the measurement back action. To this end,
we derive a quantum analog of the Euler relation, which is governed by the
information retrieved by local quantum measurements. The validity of the
relation is demonstrated for the collective dissipation model, where we find
that thermodynamic behavior is exhibited in the weak-coupling regime.
