We investigate the nonequilibrium back reaction on the Schwarzschild black hole from the radiation field. The back reactions are characterized by the membrane close to the black hole. When the membrane is thin, we found that larger temperature difference can lead to more significant negative surface tension, larger thermodynamic dissipation cost, and back reaction in energy and entropy as well as larger black hole area. This may be relevant to the primordial black holes in early universe. Moreover, our nonequilibrium model can resolve the inconsistency issue of the black hole back reaction under zero mass limit in the equilibrium case. In the thick membrane case, the nonequilibrium back reaction is found to be more significant than that in the thin membrane case. The nonequilibrium temperature difference can increase the energy and entropy loss as well as the thermodynamic dissipation of the black hole and the membrane back reactions. The nonequilibrium dissipation cost characterized by the entropy production rate appears to be significant compared to the entropy rate radiated by the black hole under finite temperature difference. This may shed light on the black hole information paradox due to the information loss from the entropy production rate in the nonequilibrium cases. The nonequilibrium thermodynamic fluctuations can also reflect the effects of the back reactions of the Hawking radiation on the evolution of a black hole.

中文翻译：

---

Schwarzschild黑洞的Hawking辐射的非平衡后反应

我们从辐射场研究了Schwarzschild黑洞上的非平衡反反应。逆反应的特征是膜靠近黑洞。当膜很薄时，我们发现更大的温差会导致更大的负表面张力，更大的热力学耗散成本以及能量和熵的逆反应以及更大的黑洞面积。这可能与早期宇宙中的原始黑洞有关。此外，我们的非平衡模型可以解决在平衡情况下零质量限制下黑洞回反应的不一致问题。在厚膜情况下，发现非平衡逆反应比在薄膜情况下更显着。非平衡温度差会增加能量和熵损失，以及黑洞的热力学耗散和膜反作用。与在有限温差下黑洞辐射的熵率相比，以熵产生率为特征的非平衡耗散成本似乎要高得多。在非平衡情况下，这可能是由于熵产生率导致的信息损失而引起的黑洞信息悖论。非平衡热力学波动也可以反映霍金辐射对黑洞演化的反作用效应。与在有限温差下黑洞辐射的熵率相比，以熵产生率为特征的非平衡耗散成本似乎要高得多。在非平衡情况下，这可能是由于熵产生率导致的信息损失而引起的黑洞信息悖论。非平衡热力学波动也可以反映霍金辐射对黑洞演化的反作用效应。与在有限温差下黑洞辐射的熵率相比，以熵产生率为特征的非平衡耗散成本似乎要高得多。在非平衡情况下，这可能是由于熵产生率导致的信息损失而引起的黑洞信息悖论。非平衡热力学波动也可以反映霍金辐射对黑洞演化的反作用效应。