The quantum square-well fluid: a thermodynamic geometric view

Abstract

We investigate several aspects of the thermodynamic geometry for a quantum fluid with square-well interactions using a third-order perturbation theory framework based on the path-integral-necklace analogy. A comparison is made between the thermodynamic and geometric properties of the quantum fluid and its classical counterpart for the interaction ranges $λ^{*}= 1.3$, 1.5, and 1.7. In particular, we analyze the scalar curvature behavior, criticality, and the corresponding Widom lines derived from curvature and several thermodynamic response functions. Quantum effects are shown to smooth supercritical anomalies of the scalar curvature and to shift its extrema for short-range interactions, while leaving the critical exponents of both the curvature and its heat capacity consistent with mean-field predictions. Widom lines associated with temperature-dependent response functions and with the curvature scalar exhibit pronounced classical-quantum differences for short interaction ranges; in contrast, those derived from the isothermal compressibility exhibit only minor variations. Overall, these results highlight the sensitivity of geometric information of thermodynamic systems due to quantum effects and the crucial role of the interaction range in shaping supercritical thermodynamic behavior.

Figures (8)

• Figure 1: Comparison of the classical and quantum supercritical isotherms of the reduced scalar curvature $R^*$ at a temperature $T^* = 1.25 T_{c}$, for $\lambda^* = 1.3$ (bottom), $\lambda^* = 1.5$ (middle) and $\lambda^* = 1.7$ (top).
• Figure 2: Comparison of the Classical and Quantum geometric spinodal lines for $\lambda^* = 1.3$ (bottom), $\lambda^* = 1.5$ (middle), and $\lambda^* = 1.7$ (upper).
• Figure 3: Critical behavior for the classical and quantum square-well curvature $R^{*}$ (upper) and $C_P$ (bottom). Both quantities are evaluated along the critical isochore ($\eta = \eta_{\text{cr}}$), as temperature approaches the critical point from above from $102\%$ to $100.002\%$ its critical value for $\lambda^* = 1.3,1.5,1.7$.
• Figure 4: Comparison of the classical and quantum $R$-Widom lines for $\lambda^* = 1.3$ (bottom), $\lambda^* = 1.5$ (middle), and $\lambda^* = 1.7$ (top).
• Figure 5: Comparison of the Classical and Quantum Zeno lines for $\lambda^* = 1.3$ (bottom), $\lambda^* = 1.5$ (middle), and $\lambda^* = 1.7$ (upper).