作为广义黑洞熵中热力学一致性判据的兰道尔原理
Landauer's Principle as a Criterion for Thermodynamic Consistency in Generalized Black Hole Entropies
AI总结：
研究利用兰道尔原理检验广义黑洞熵关系的热力学一致性，对贝肯斯坦 - 霍金熵等模型分析得出三种结果，推导兼容模型的面积量子化参数和谱，揭示了信息论与黑洞热力学的深层联系。
AI中文摘要：
在黑洞视界面积量子化的假设下，黑洞霍金蒸发的每一步，即黑洞质量损失并跃迁到更低面积水平，被解释为一位信息的擦除。本文利用兰道尔原理，检验各种黑洞熵关系与该信息论框架的一致性。对于贝肯斯坦 - 霍金熵，每步发射的能量达到兰道尔极限。我们将此分析扩展到一大类广义熵模型，得出三种不同结果。第一类中，兰道尔原理对霍金温度进而对黑洞质量施加限制；第二类限制熵模型的自由参数；第三类如卡尼亚达基斯熵与兰道尔原理不相容。对于所有兼容模型，我们推导了面积量子化参数和相应的面积谱。虽然该参数对贝肯斯坦 - 霍金熵是常数，但对许多广义模型它与能级数有关。不过，连续面积水平之间的相对间距在经典极限中消失。我们的发现表明信息论与黑洞热力学之间存在深刻联系。
英文摘要：
Under the assumption that black hole horizon area is quantized, each Hawking evaporation step, during which the black hole loses mass and transitions to a lower area level, is interpreted as the erasure of one bit of information. In this paper, by employing Landauer's principle, we test the consistency of various black hole entropy relations with this information-theoretic framework. For the Bekenstein-Hawking entropy, the energy emitted per step saturates the Landauer bound. We extend this analysis to a broad class of generalized entropy models, yielding three distinct outcomes. In the first category, Landauer's principle imposes constraints on the Hawking temperature and, consequently, on the black hole mass. In the second, it restricts the free parameters of the entropy model. The third category, exemplified by Kaniadakis entropy, proves incompatible with Landauer's principle. For all compatible models, we derive the area quantization parameter and the corresponding area spectrum. While this parameter is constant for Bekenstein-Hawking entropy, it becomes level-number-dependent for many generalized models. Nonetheless, the relative spacing between successive area levels vanishes in the classical limit. Our findings point to a deep link between information theory and black hole thermodynamics.
