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

TL;DR

This paper demonstrates that the generalized Gr"uneisen ratio, when formulated with non-additive $q$-entropy, remains finite at critical points, resolving the long-standing issue of perceived divergence in thermodynamic susceptibilities.

Contribution

It introduces a universal non-diverging Gr"uneisen ratio based on $q$-entropy at critical points, extending previous classical and quantum formulations.

Findings

The generalized Gr"uneisen ratio is non-diverging at critical points when using $S_q$.

The formulation recovers the classical BG case as $q ightarrow 1$.

Addresses the problem of illusory divergence of susceptibilities at critical points.

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.