黏性变广义Chaplygin气体的热力学稳定性
Thermodynamic Stability of a Viscous Variable Generalised Chaplygin Gas
- Netaji Nagar Day College（纳塔贾·纳加尔日学院）
- Jadavpur University（贾达普大学）
- GLA University（GLA大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究探讨黏性变广义Chaplygin气体模型的宇宙学与热力学性质，发现负黏性参数下模型从早期减速过渡到晚期类幻影加速，并满足热力学稳定性，与观测数据吻合。
AI中文摘要：
我们在空间平坦的Friedmann-Lemaître-Robertson-Walker宇宙中研究了黏性变广义Chaplygin气体（VVGCG）模型的宇宙学动力学和热力学性质，该模型由$P=-B/\rho^\alpha$描述，其中$B=B_0V^{n/3}$。该模型包含体黏性压力$\Pi=-3\xi H$，其中$\xi=\xi_0\rho^{1/2}$。我们发现物理上可行的分支对应于$\xi_0<0$，此时正黏性压力在早期占主导，产生减速膨胀。随着体积增加，有效压力在有限体积$V_c$处改变符号，而向加速的转变发生在更大的体积$V_f$处。在大体积下，状态方程参数在$n<0$时接近类幻影（phantom-like）区域。对热状态方程和量热状态方程、熵、热容量以及等温和绝热稳定性的详细热力学分析表明，对于$n<0$和$\xi_0<0$，稳定性条件和$c_V>0$同时满足。熵在$T\rightarrow0$时消失，与热力学第三定律一致，而该模型允许有限的最小体积和相应的最大温度。热力学一致性通过基本热力学恒等式进一步验证。该框架还包含几种现有的Chaplygin气体模型作为特例。来自Hubble-57数据的约束给出$\alpha=0.0024$，$n=-0.0182$，$\xi_0=-0.0015$，与热力学稳定参数区域一致。因此，VVGCG模型提供了从早期减速阶段到晚期类幻影加速的宇宙演化的自洽描述，并在整个演化过程中保持热力学稳定。
英文摘要：
We investigate the cosmological dynamics and thermodynamic properties of a viscous variable generalized Chaplygin gas (VVGCG) model in a spatially flat Friedmann--Lema^ıtre--Robertson--Walker universe, described by $P=-B/ρ^α$, where $B=B_0V^{n/3}$. The model includes a bulk-viscous pressure $Π=-3ξH$, with $ξ=ξ_0ρ^{1/2}$. We find that the physically viable branch corresponds to $ξ_0<0$, for which the positive viscous pressure dominates at early times, producing decelerated expansion. As the volume increases, the effective pressure changes sign at a finite volume $V_c$, while the transition to acceleration occurs at a larger volume $V_f$. At large volume, the equation-of-state parameter approaches a phantom-like regime for $n<0$. A detailed thermodynamic analysis of the thermal and caloric equations of state, entropy, heat capacity, and isothermal and adiabatic stability shows that the stability conditions and $c_V>0$ are simultaneously satisfied for $n<0$ and $ξ_0<0$. The entropy vanishes as $T\rightarrow0$, consistent with the third law, while the model admits a finite minimum volume and corresponding maximum temperature. Thermodynamic consistency is further verified through the fundamental thermodynamic identity. The framework also contains several existing Chaplygin-gas models as special cases. Constraints from the Hubble-57 data yield $α=0.0024$, $n=-0.0182$, and $ξ_0=-0.0015$, consistent with the thermodynamically stable parameter region. Thus, the VVGCG model provides a consistent description of cosmic evolution from an early decelerating phase to late-time phantom-like acceleration while remaining thermodynamically stable throughout the evolution.
