Title: Viability of Variable Generalised Chaplygin gas - a thermodynamical approach Show Chinese title

Title: 变量广义 Chaplygin 气体的可行性 - 热力学方法

Abstract: The viability of the variable generalised Chaplygin gas (VGCG) model is analysed from the standpoint of its thermodynamical stability criteria with the help of an equation of state, $P = - \frac{B}{\rho^{\alpha}}$, where $B = B_{0}V^{-\frac{n}{3}}$. Here $B_{0}$ is assumed to be a positive universal constant, $n$ is a constant parameter and $V$ is the volume of the cosmic fluid. We get the interesting result that if the well-known stability conditions of a fluid is adhered to, the values of $n$ are constrained to be negative definite to make $ \left(\frac{\partial P}{\partial V}\right)_{S} <0$ \& $ \left(\frac{\partial P}{\partial V}\right)_{T} <0$ throughout the evolution. Moreover the positivity of thermal capacity at constant volume $c_{V}$ as also the validity of the third law of thermodynamics are ensured in this case. For the particular case $n = 0$ the effective equation of state reduces to $\Lambda$CDM model in the late stage of the universe while for $n <0$ it mimics a phantom-like cosmology which is in broad agreement with the present SNe Ia constraints like VGCG model. The thermal equation of state is discussed and the EoS parameter is found to be an explicit function of temperature only. Further for large volume the thermal equation of state parameter is identical with the caloric equation of state parameter when $ T \rightarrow 0$. It may also be mentioned that like Santos et al our model does not admit of any critical points. We also observe that although the earlier model of Lu explains many of the current observational findings of different probes it fails to explain the crucial tests of thermodynamical stability. Show Chinese abstract

Abstract: 从热力学稳定性准则的角度分析了变分广义查普林模型（VGCG）模型的可行性，借助状态方程$P = - \frac{B}{\rho^{\alpha}}$，其中$B = B_{0}V^{-\frac{n}{3}}$。此处假设$B_{0}$是一个正的普遍常数，$n$是一个常数参数，$V$是宇宙流体的体积。 如果我们遵循流体的著名稳定性条件，那么$n$的值被限制为负定，以使$ \left(\frac{\partial P}{\partial V}\right)_{S} <0$&$ \left(\frac{\partial P}{\partial V}\right)_{T} <0$在整个演化过程中保持稳定。 此外，在这种情况下，恒定体积下的热容量$c_{V}$的正性以及热力学第三定律的有效性也得到了保证。 对于特殊情况$n = 0$，有效状态方程在宇宙晚期简化为$\Lambda$CDM 模型，而对于$n <0$，它模仿一种类奇异物质宇宙学，这与目前的超新星 Ia 约束（如 VGCG 模型）大致一致。 讨论了热力学状态方程，发现状态方程参数仅是温度的显式函数。 对于大体积，当$ T \rightarrow 0$时，热力学状态方程参数与热力学状态方程参数是相同的。 也可以指出，类似于 Santos 等人的模型，我们的模型不包含任何临界点。 我们还观察到，尽管 Lu 的早期模型解释了不同探针的当前观测结果，但它无法解释热力学稳定性的关键测试。