In this paper, we present a review of some recent results concerning the thermal corrections to the Casimir energy of massless scalar, electromagnetic, and massless spinor fields in the Einstein and closed Friedmann universes with a cosmic string. In the case of a massless scalar field, it is shown that the Casimir energy can be written as a simple sum of two terms; the first one corresponds to the Casimir energy for the massless scalar field in the Einstein and Friedmann universes without a cosmic string, whereas the second one is simply the Casimir energy of the electromagnetic in this background, multiplied by a parameter $\lambda =(1/\alpha )-1$, where $\alpha$ is a constant that codifies the presence of the cosmic string, and is related to its linear mass density, $\mu$, by the expression $\alpha =1-G\mu$. The Casimir free energy and the internal energy at a temperature different from zero, as well as the Casimir entropy, are given by similar sums. In the cases of the electromagnetic and massless spinor fields, the Casimir energy, free energy, internal energy, and Casimir entropy are also given by the sum of two terms, similarly to the previous cases, but now with both terms related to the same field. Using the results obtained concerning the mentioned thermodynamic quantities, their behavior at high and low temperatures limits are studied. All these results are particularized to the scenario in which the cosmic string is absent. Some discussions concerning the validity of the Nernst heat theorem are included as well.

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关于爱因斯坦和具有宇宙弦的封闭弗里德曼宇宙中的卡西米尔热效应的一些结果的评论

在本文中，我们回顾了一些最近的结果，这些结果涉及对爱因斯坦和具有宇宙弦的封闭弗里德曼宇宙中的无质量标量、电磁和无质量自旋量场的卡西米尔能量进行热校正。在无质量标量场的情况下，卡西米尔能量可以写成两项的简单和；第一个对应于爱因斯坦和弗里德曼宇宙中没有宇宙弦的无质量标量场的 Casimir 能量，而第二个则只是这个背景中电磁场的 Casimir 能量乘以一个参数$\lambda =(1/\alpha )-1$， 在哪里 $\alpha$ 是一个常数，用于编码宇宙弦的存在，并与它的线性质量密度有关， $\mu$，由表达式 $\alpha =1-G\mu$. 卡西米尔自由能和非零温度下的内能以及卡西米尔熵由类似的总和给出。在电磁场和无质量自旋场的情况下，卡西米尔能、自由能、内能和卡西米尔熵也由两项之和给出，与前面的情况类似，但现在这两项都与同一场有关. 使用获得的关于上述热力学量的结果，研究了它们在高温和低温极限下的行为。所有这些结果都特定于宇宙弦不存在的场景。还包括一些关于能斯特热定理有效性的讨论。