腔体内渐近平坦黑洞的状态切换热力学与动力学
Thermodynamics and kinetics of state switching for the asymptotically flat black hole in a cavity
AI总结：
本文利用自由能景观形式研究腔体内渐近平坦黑洞的状态切换，推导广义自由能并获得相图，揭示无电荷黑洞的霍金-佩奇型相变和带电黑洞的范德瓦尔斯型相变，并分析切换动力学由温度和势垒高度决定。
摘要：
我们提出，可以通过自由能景观形式来研究由腔体包围的渐近平坦黑洞的状态切换热力学与动力学。利用York方法，推导了正则系综中腔体内黑洞的广义自由能，其中腔体上的温度和腔体内的电荷保持为固定参数。通过量化相应的自由能景观，我们获得了腔体内黑洞的相图，揭示了无电荷黑洞的霍金-佩奇型相变和带电黑洞的范德瓦尔斯型相变。我们进一步假设，黑洞状态切换的动力学由自由能景观产生的梯度力和热噪声产生的随机力共同决定。然后，我们推导了首次通过时间分布函数的$n$阶矩的递推关系，从而能够计算以平均首次通过时间及其相对涨落为特征的动力学时间。我们的分析表明，黑洞状态切换的动力学由系综温度和自由能景观上的势垒高度决定。
英文摘要：
We propose that the thermodynamics and the kinetics of state switching for the asymptotically flat black hole enclosed by a cavity can be studied in terms of the free energy landscape formalism. The generalized free energy for the black hole enclosed by a cavity in the canonical ensemble is derived by using the York's approach, where the temperature on the cavity and the charges inside the cavity are kept as the fixed parameters. By quantifying the corresponding free energy landscape, we obtain the phase diagrams for the black hole in cavity, which reveal a Hawking-Page type transition for the uncharged black hole and a Van der Waals type transition for the charged black hole. We further assume that the dynamics of black hole state switching is mutually determined by the gradient force and the stochastic force arising from the free energy landscape and the thermal noises respectively. We then derive a recurrence relation for the $n$-momentum of the first passage time distribution function, which enables the calculation of the kinetic times characterized by the mean first passage time and its relative fluctuation. Our analysis illustrates that the kinetics of black hole state switching is determined by the ensemble temperature and the barrier height on the free energy landscape.
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