A correspondence between fluctuations of non-minimally coupled scalar fields and that of an effective fluid with heat flux and anisotropic stresses, is shown. Though the correspondence between respective stress tensors of scalar fields and fluids is known and widely used in literature, the fluctuations in the two cases still await a formal correspondence and are open to investigation in all details. Using results obtained in the newly established theory of semiclassical stochastic gravity which focuses on the fluctuations of the quantum stress tensor, we show new relations in this regard. This development, apart from its relevance to the field-fluid correspondence, is expected to give insight to the mesoscopic phenomena for gravitating systems, and enable backreaction studies of the fluctuations on the perturbations of astrophysical objects. Such a development is aimed to enhance the perturbative analysis for cosmological spacetimes and astrophysical objects specifically in the decoherence limit. A kinetic theory, which can be based on stochastic fluctuations vs particle picture in curved spacetime may find useful insights from such correspondences in future work.

中文翻译：

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退相干极限下半经典和经典引力物质场涨落的对应关系

显示了非最小耦合标量场的波动与具有热通量和各向异性应力的有效流体的波动之间的对应关系。尽管标量场和流体各自的应力张量之间的对应关系是已知的并且在文献中被广泛使用，但这两种情况下的波动仍在等待正式的对应关系，并且可以进行所有细节的调查。利用新建立的半经典随机引力理论中获得的结果，该理论侧重于量子应力张量的波动，我们展示了这方面的新关系。这一发展，除了与场-流体对应的相关性外，有望深入了解引力系统的介观现象，并能够对天体物理物体扰动的波动进行反向反应研究。这样的发展旨在加强对宇宙时空和天体物理物体的微扰分析，特别是在退相干极限。可以基于随机波动与弯曲时空中的粒子图的动力学理论可能会在未来的工作中从这种对应关系中找到有用的见解。