The fundamental equation of the thermodynamic system gives the relation between internal energy, entropy and volume of two adjacent equilibrium states. Taking higher dimensional charged Gauss-Bonnet black hole in de Sitter space as a thermodynamic system, the state parameters have to meet the fundamental equation of thermodynamics. We introduce the effective thermodynamic quantities to describe the black hole in de Sitter space. Considering that in the lukewarm case the temperature of the black hole horizon is equal to that of the cosmological horizon, the effective temperature of spacetime is the same, we conjecture that the effective temperature has the same value. In this way, we can obtain the entropy formula of spacetime by solving the differential equation. We find that the total entropy contain an extra terms besides the sum of the entropies of the two horizons. The corrected terms of the entropy is a function of horizon radius ratio, and is independent of the charge of the spacetime.

中文翻译：

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德西特空间中高维带电 Gauss-Bonnet 黑洞的熵

热力学系统的基本方程给出了两个相邻平衡态的内能、熵和体积之间的关系。以德西特空间的高维带电Gauss-Bonnet黑洞作为热力学系统，其状态参数必须满足热力学基本方程。我们引入了有效热力学量来描述德西特空间中的黑洞。考虑到在微温情况下黑洞视界的温度等于宇宙学视界的温度，时空的有效温度相同，我们推测有效温度具有相同的值。这样，我们就可以通过求解微分方程得到时空的熵公式。我们发现总熵除了两个视界的熵之和外还包含一个额外的项。熵的修正项是视界半径比的函数，与时空电荷无关。