In this paper, firstly, the conditions and existence region for the coexistence of the black hole and cosmological horizons in Non-linear charged dS (NLC-dS) spacetime are discussed, subsequently, the thermodynamic quantities for which the boundary conditions are satisfied in spacetime in the coexistence region of the two horizons are discussed, and the effective thermodynamic quantities in the NLC-dS spacetime in the coexistence region with two horizons are presented. Based on these, the heat capacity in the coexistence region with two horizons is addressed, the behavior of the heat capacity in the NLC-dS spacetime in the aforementioned region is found to exhibit the characteristics of Schottky specific heat. In order to investigate the intrinsic reason of the heat capacity in spacetime, we regard the two horizons in the NLC-dS spacetime as two distinct energy levels, consequently, the microscopic particles at different horizons exhibit disparate energies. Using the heat capacity relationship between the two-energy levels in an ordinary thermodynamic system, the heat capacity in dS spacetime is discussed, it is observed that the behavior of the heat capacity is analogous to that of the two-energy levels in an ordinary thermodynamic system. The number of microscopic particles in the two-energy-level system are approximated by comparing the maximum value of the heat capacity of the system with the maximum value obtained by treating the two horizons in the NLC-dS spacetime as a two-energy-level system of two distinct energies. This conclusion reflects the quantum properties of the coexistence region with two horizons in the NLC-dS spacetime. It provides a new avenue for further study of the thermodynamic properties of black holes and the quantum properties of de Sitter spacetime.

中文翻译：

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非线性带电 dS 时空及其热力学和肖特基异常


本文首先讨论了非线性电荷 dS （NLC-dS） 时黑洞和宇宙视界共存的条件和存在区域，然后讨论了两个视界共存区中满足时空边界条件的热力学量，并给出了两个视界共存区中 NLC-dS 时空的有效热力学量。基于这些，解决了两个层位共存区域的热容问题，发现上述区域 NLC-dS 时空的热容行为表现出肖特基比热的特性。为了探究时空热容的内在原因，我们将 NLC-dS 时空中的两个视界视为两个不同的能级，因此，不同视界的微观粒子表现出不同的能量。利用普通热力学系统中两个能级之间的热容关系，讨论了 dS 时空的热容，观察到热容的行为类似于普通热力学系统中两个能级的行为。通过将系统的热容量最大值与将 NLC-dS 时空中的两个层位视为两种不同能量的双能级系统获得的最大值进行比较，近似计算出双能级系统中微观粒子的数量。这一结论反映了 NLC-dS 时空中两个视界共存区域的量子性质。 它为进一步研究黑洞的热力学特性和 de Sitter 时空的量子特性提供了一条新的途径。