Quantum capacity and vacuum compressibility of spacetime: Thermal fields

doi:10.3390/universe8050291

機構典藏 > College of Sciences > Graduate Institute & Department of Physics > Journal Article > Item 987654321/123348

Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/123348

Title:	Quantum capacity and vacuum compressibility of spacetime: Thermal fields
Authors:	Hing-Tong Cho, Jen-Tsung Hsiang, Bei-Lok Hu
Keywords:	quantum fields;curved spacetime;heat capacity;vacuum compressibility
Date:	2022-05-21
Issue Date:	2023-04-28 17:46:27 (UTC+8)
Publisher:	MDPI AG
Abstract:	An important yet perplexing result from work in the 1990s and 2000s is the near-unity value of the ratio of fluctuations in the vacuum energy density of quantum fields to the mean in a collection of generic spacetimes. This was carried out by way of calculating the noise kernels which are the correlators of the stress-energy tensor of quantum fields. In this paper, we revisit this issue via a quantum thermodynamics approach, by calculating two quintessential thermodynamic quantities: the heat capacity and the quantum compressibility of some model geometries filled with a quantum field at high and low temperatures. This is because heat capacity at constant volume gives a measure of the fluctuations of the energy density to the mean. When this ratio approaches or exceeds unity, the validity of the canonical distribution is called into question. Likewise, a system’s compressibility at constant pressure is a criterion for the validity of grand canonical ensemble. We derive the free energy density and, from it, obtain the expressions for these two thermodynamic quantities for thermal and quantum fields in 2d Casimir space, 2d Einstein cylinder and 4d (S1×S3 ) Einstein universe. To examine the dependence on the dimensionality of space, for completeness, we have also derived these thermodynamic quantities for the Einstein universes with even-spatial dimensions: S1×S2 and S1×S4. With this array of spacetimes we can investigate the thermodynamic stability of quantum matter fields in them and make some qualitative observations on the compatibility condition for the co-existence between quantum fields and spacetimes, a fundamental issue in the quantum and gravitation conundrum.
Relation:	Universe 8(5), 291
DOI:	10.3390/universe8050291
Appears in Collections:	[Graduate Institute & Department of Physics] Journal Article

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