标题： 黑洞相变的广义自由能景观 显示英文标题

标题： Generalized free energy landscape of black hole phase transition

摘要： 近日，基于自由能景观的随机动力学模型被提出以量化黑洞相变的 kinetics。 一个核心概念是波动黑洞的广义自由能，该概念以前通过热力学关系定义。 在这项工作中，通过采用Gibbons-Hawking路径积分方法处理黑洞热力学，我们展示了广义自由能可以从具有锥形奇点的欧几里得引力瞬子的爱因斯坦-希尔伯特作用中推导出来。 这项工作为黑洞相变的自由能景观形式主义提供了坚实的基础。 显示英文摘要

摘要： Recently, the stochastic dynamical model based on the free energy landscape was proposed to quantify the kinetics of the black hole phase transition. An essential concept is the generalized free energy of the fluctuating black hole, which was defined in terms of the thermodynamic relation previously. In this work, by employing the Gibbons-Hawking path integral approach to black hole thermodynamics, we show that the generalized free energy can be derived from the Einstein-Hilbert action of the Euclidean gravitational instanton with the conical singularity. This work provides a concrete and solid foundation for the free energy landscape formalism of black hole phase transition.