The Gr\"uneisen ratio Γ, i.e., the singular part of the ratio of
thermal expansion to the specific heat, has been broadly employed to explore
both finite-T and quantum critical points (QCPs). For a genuine quantum phase
transition (QPT), thermal fluctuations are absent and thus the thermodynamic
Γ cannot be employed. We propose a quantum analogue to Γ that
computes entanglement as a function of a tuning parameter and show that QPTs
take place only for quadratic non-diagonal Hamiltonians. We showcase our
approach using the quantum 1D Ising model with transverse field and Kane's
quantum computer. The slowing down of the dynamics and thus the ``creation of
mass'' close to any QCP/QPT is also discussed.Comment: 5 pages, 3 figures, comments are wellcome