In this letter, we show that the Semiclassical Einstein’s Field Equation can be recovered using the generalized entropy \(S_{gen}\). This approach is reminiscent of non-equilibrium thermodynamics. Furthermore, contrary to the entanglement equilibrium approach of deriving the semiclassical Einstein’s equation, this approach does not require any such assumptions and still recovers its correct form. Therefore, in a sense, we also show the validity of the semiclassical approximation, a crucial approach for establishing a number of important ideas such as the Hawking effect.

中文翻译：

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使用广义熵恢复半经典爱因斯坦方程

在这封信中，我们证明可以使用广义熵\(S_{gen}\)恢复半经典爱因斯坦场方程。这种方法让人想起非平衡热力学。此外，与推导半经典爱因斯坦方程的纠缠平衡方法相反，该方法不需要任何此类假设，并且仍然恢复其正确的形式。因此，从某种意义上说，我们也证明了半经典近似的有效性，这是建立霍金效应等许多重要思想的关键方法。