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: S 1 × S 2 and S 1 × S 4. 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 ( S 1 × S 3 ) Einstein universe. Likewise, a system’s compressibility at constant pressure is a criterion for the validity of grand canonical ensemble. When this ratio approaches or exceeds unity, the validity of the canonical distribution is called into question. This is because heat capacity at constant volume gives a measure of the fluctuations of the energy density to the mean. 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 was carried out by way of calculating the noise kernels which are the correlators of the stress-energy tensor of quantum fields. Authors may use MDPI'sĮnglish editing service prior to publication or during author revisions.Īn 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. Submitted papers should be well formatted and use good English. Please visit the Instructions for Authors page before submitting a manuscript. Universe is an international peer-reviewed open access monthly journal published by MDPI. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. All manuscripts are thoroughly refereed through a single-blind peer-review process. Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website. Research articles, review articles as well as short communications are invited. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. All submissions that pass pre-check are peer-reviewed. Manuscripts can be submitted until the deadline. Once you are registered, click here to go to the submission form. Manuscripts should be submitted online at by registering and logging in to this website. We are interested in collecting contributions on a broad range of approaches and ideas which emphasize the quantum nature of the primordial universe and related issues, like time problem in quantum gravity. We believe that such frameworks have a potential to explain the initial conditions as well as the origin of the expansion in the Universe without inevitably postulating fine-tuned primordial fields. We wish to invite both original and review papers to this Special Issue, which particularly emphasize ideas and problems of frameworks based on background independent quantum cosmology. It is worth noting that future experiments that aim at detecting and measuring primordial gravitational waves may soon further constrain the primordial state of the Universe. Thus, we need a better theory that can at once resolve the singularity problem and explain the peculiar primordial universe that has started the present cosmological expansion. Nevertheless, it is commonly accepted that general relativity (and hence ΛCDM) breaks down near the singularity. The existing data and available models point to the ΛCDM model of expanding universe starting at the big bang singularity 13.7 billion years ago in a nearly homogeneous, state with tiny and Gaussian matter inhomogeneities over superhorizon scales. The Special Issue is aimed at collecting contributions on all aspects of quantum cosmology, including singularity resolutions, problem of time, semiclassical descriptions, methods of quantization of cosmological models, and quantum cosmological alternatives to inflationary models.
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