Universally non-diverging Gr\"uneisen parameter at critical points

Samuel M. Soares; Lucas Squillante; Henrique S. Lima; Constantino Tsallis; Mariano de Souza

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arXiv · 2409.11086

Universally non-diverging Gr\"uneisen parameter at critical points

Samuel M. Soares·Lucas Squillante·Henrique S. Lima·Constantino Tsallis·Mariano de Souza

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Abstract

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 $\Gamma$. Motivated by the results reported in Phys. Rev. B $\textbf{108}$, L140403 (2023), we extend the quantum version of $\Gamma$ to the non-additive $q$-entropy $S_q$. Our findings indicate that using $S_q$ at the unique value of $q$ restoring the extensivity of the entropy, $\Gamma$ is universally non-diverging at CPs. We unprecedentedly introduce $\Gamma$ in terms of $S_q$, being BG recovered for $q \rightarrow 1$. We thus solve a long-standing problem related to the $\textit{illusory}$ diverging susceptibilities at CPs.

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Samuel M. Soares, Lucas Squillante, Henrique S. Lima, Constantino Tsallis, Mariano de Souza. 2024-09-17. Universally non-diverging Gr\"uneisen parameter at critical points. https://arxiv.org/abs/2409.11086

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