Universally nondiverging Grüneisen parameter at critical points

According to Boltzmann-Gibbs (BG) statistical mechanics, the thermodynamic response, such as the isothermal susceptibility, at critical points (CPs) presents a divergent-like behavior. An appropriate parameter to probe both classical and quantum CPs is the so-called Gr"uneisen ratio $\mathrm{\ensuremath{\Gamma}}$. Motivated by the results reported in [Phys. Rev. B 108, L140403 (2023)], we extend the quantum version of $\mathrm{\ensuremath{\Gamma}}$ to the nonadditive $q$-entropy ${S}_{q}$. Our findings indicate that using ${S}_{q}$ at the unique value of $q$ restoring the extensivity of the entropy, $\mathrm{\ensuremath{\Gamma}}$ is universally nondiverging at CPs. We unprecedentedly introduce $\mathrm{\ensuremath{\Gamma}}$ in terms of ${S}_{q}$, being BG recovered for $q\ensuremath{\rightarrow}1$. We thus solve a long-standing problem related to the illusory diverging susceptibilities at CPs.