标题： 动态时空的比热容和量子压缩性与热粒子产生 显示英文标题

标题： Heat capacity and quantum compressibility of dynamical spacetimes with thermal particle creation

摘要： 这项工作继续研究了两篇近期论文中关于时空量子热力学的内容，1) 将[1]中在早期宇宙宇宙学背景下研究的热量子场置于更广泛的背景中，2) 将[2]中处理动态空间真空压缩性的考虑扩展到具有热量子场的动态时空。 我们首先指出，在动态设置中，热平衡条件并不保证存在或维持，因此在宇宙学时空中的有限温度量子场论需要比教科书中通常描述的更为谨慎的考虑。 完整的描述需要使用“in-in”技术在动态时空中进行非平衡量子场论。 一个更易处理的动力学子类是热平衡条件在演化开始和结束时都明确定义的情况。 在这里我们将假设一个in-真空态。 已经证明，如果中间动力学有一个指数膨胀的初始时期，如在暴胀宇宙学中，从初始真空中真空涨落的参数放大产生的粒子在out态测量时将具有热谱。 在这些条件下，可以应用有限温度场论来计算量子热力学量。 这里我们考虑基于简单解析可解的Bernard-Duncan模型的闭合四维弗里德曼-勒梅特-罗伯逊-沃尔克宇宙中的一个质量规范标量场。 我们计算了从in-真空产生的粒子的能量密度并推导了配分函数。 从自由能我们接着推导了具有热粒子产生的时空的比热和量子压缩性。 最后我们对该研究计划进行了一些讨论并提出了进一步工作的建议。 显示英文摘要

摘要： This work continues the investigation in two recent papers on the quantum thermodynamics of spacetimes, 1) placing what was studied in [1] for thermal quantum fields in the context of early universe cosmology, and 2) extending the considerations of vacuum compressibility of dynamical spaces treated in [2] to dynamical spacetimes with thermal quantum fields. We begin with a warning that thermal equilibrium condition is not guaranteed to exist or maintained in a dynamical setting and thus finite temperature quantum field theory in cosmological spacetimes needs more careful considerations than what is often described in textbooks. A full description requires nonequilibrium quantum field theory in dynamical spacetimes using `in-in' techniques. A more manageable subclass of dynamics is where thermal equilibrium conditions are established at both the beginning and the end of evolution are both well defined. Here we shall assume an in-vacuum state. It has been shown that if the intervening dynamics has an initial period of exponential expansion, such as in inflationary cosmology, particles created from the parametric amplification of the vacuum fluctuations in the initial vacuum will have a thermal spectrum measured at the out-state. Under these conditions finite temperature field theory can be applied to calculate the quantum thermodynamic quantities. Here we consider a massive conformal scalar field in a closed four-dimensional Friedmann-Lemaitre-Robertson-Walker universe based on the simple analytically solvable Bernard-Duncan model. We calculate the energy density of particles created from an in-vacuum and derive the partition function. From the free energy we then derive the heat capacity and the quantum compressibility of the spacetimes with thermal particle creation. We end with some discussions and suggestions for further work in this program of studies.