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 Grüneisen ratio $\mathrm{\Gamma }$. Motivated by the results reported in [Phys. Rev. B 108, L140403 (2023)], we extend the quantum version of $\mathrm{\Gamma }$ 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, $\mathrm{\Gamma }$ is universally nondiverging at CPs. We unprecedentedly introduce $\mathrm{\Gamma }$ in terms of $S_q$, being BG recovered for $q\to 1$. We thus solve a long-standing problem related to the illusory diverging susceptibilities at CPs.

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• Classical statistical mechanics
• Continuous phase transition
• Critical phenomena
• Entropy
• Ising model