--- title: "Quantum Bound on the Specific Entropy in Strong-Coupled Scalar Field Theory • CBPF Index" description: "CBPF INDEX is the system that tracks the scientific and technological output of CBPF. It lists the articles, books, technical reports and other publications of the whole CBPF community." canonical_url: "https://index.cbpf.br/en/publicacoes/6ad2a767639f62b11adbb02f" locale: en meta: "og:description": "CBPF INDEX is the system that tracks the scientific and technological output of CBPF. It lists the articles, books, technical reports and other publications of the whole CBPF community." "og:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_Quantum%2BBound%2Bon%2Bthe%2BSpecific%2BEntropy%2Bin%2BStrong-Coupled%2BScalar%2BField%2BTheory%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_~TS4gQXBhcmljaW8gQWxjYWxkZTsgRy4gTWVuZXplczsgTi5GLiBTdmFpdGVy%2Cdetalhe_~MDIvMDgvMjAxMA%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmIwMmYi%2Cs_T4-JzOvmTemdCXrf.png" "og:image:height": "600" "og:image:type": image/png "og:image:width": "1200" "og:title": "Quantum Bound on the Specific Entropy in Strong-Coupled Scalar Field Theory • CBPF Index" "twitter:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_Quantum%2BBound%2Bon%2Bthe%2BSpecific%2BEntropy%2Bin%2BStrong-Coupled%2BScalar%2BField%2BTheory%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_~TS4gQXBhcmljaW8gQWxjYWxkZTsgRy4gTWVuZXplczsgTi5GLiBTdmFpdGVy%2Cdetalhe_~MDIvMDgvMjAxMA%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmIwMmYi%2Cs_T4-JzOvmTemdCXrf.png" --- > Index of every page on this site: [llms.txt](https://index.cbpf.br/llms.txt) **Physics Note****Published** # **Quantum Bound on the Specific Entropy in Strong-Coupled Scalar Field Theory** **M. Aparicio Alcalde; G. Menezes; N.F. Svaiter** 08/02/2010 [**Download PDF **0.2 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbb02f/pdf) [**Contact owner**](mailto:apub@cbpf.br?subject=Quantum%20Bound%20on%20the%20Specific%20Entropy%20in%20Strong-Coupled%20Scalar%20Field%20Theory) ## **Publication details**
Authors
M. Aparicio Alcalde; G. Menezes; N.F. Svaiter
Type
Physics Note
Status
Published
Publication date
02/08/2010
Description
Using the Euclidean path integral approach with functional methods, we discuss the $(g_{0}\,\varphi^{\,p})_{d}$ self-interacting scalar field theory, in the strong-coupling regime. We assume the presence of macroscopic boundaries confining the field in a hypercube of side $L$. We also consider that the system is in thermal equilibrium at temperature $\beta^{\,-1}$. For spatially bounded free fields, the Bekenstein bound states that the specific entropy satisfies the inequality $\frac{S}{E} < 2 \pi R$, where $R$ stands for the radius of the smallest sphere that circumscribes the system. Employing the strong-coupling perturbative expansion, we obtain the renormalized mean energy $E$ and entropy $S$ for the system up to the order $(g_{0})^{-\frac{2}{p}}$, presenting an analytical proof that the specific entropy also satisfies in some situations a quantum bound. Defining $\varepsilon_d^{(r)}$ as the renormalized zero-point energy for the free theory per unit length, the dimensionless quantity $\xi=\frac{\beta}{L}$ and $h_1(d)$ and $h_2(d)$ as positive analytic functions of $d$, for the case of high temperature, we get that the specific entropy satisfies $\frac{S}{E} < 2\pi R\,\frac{h_1(d)}{h_2(d)}\,\xi$. When considering the low temperature behavior of the specific entropy, we have $\frac{S}{E} <2\pi R\, \frac{h_1(d)}{\varepsilon_d^{(r)}}\xi^{\,1-d}$. Therefore the sign of the renormalized zero-point energy can invalidate this quantum bound. If the renormalized zero point-energy is a positive quantity, at intermediate temperatures and in the low temperature limit, there is a quantum bound.
Year
2007
Number
CBPF-NF-022/07
Linked to a thesis
No
Linked to a grant
No
```json {"@context":"https://schema.org","@graph":[{"@id":"https://index.cbpf.br/en#website","@type":"WebSite","description":"O CBPF INDEX é o sistema de acompanhamento da produção científica e tecnológica do CBPF. Nele é possível obter a lista de publicações de artigos, livros, relatórios técnicos, etc de toda a comunidade do CBPF.","inLanguage":"en-US","name":"CBPF Index","url":"https://index.cbpf.br/en","publisher":{"@id":"https://index.cbpf.br/#identity"},"translationOfWork":{"@id":"https://index.cbpf.br/#website"}},{"@id":"https://index.cbpf.br/en/publicacoes/6ad2a767639f62b11adbb02f#webpage","@type":"WebPage","description":"CBPF INDEX is the system that tracks the scientific and technological output of CBPF. It lists the articles, books, technical reports and other publications of the whole CBPF community.","name":"Quantum Bound on the Specific Entropy in Strong-Coupled Scalar Field Theory","url":"https://index.cbpf.br/en/publicacoes/6ad2a767639f62b11adbb02f","isPartOf":{"@id":"https://index.cbpf.br/en#website"},"potentialAction":[{"@type":"ReadAction","target":["https://index.cbpf.br/en/publicacoes/6ad2a767639f62b11adbb02f"]}],"primaryImageOfPage":{"@id":"https://index.cbpf.br/#logo"}},{"@id":"https://index.cbpf.br/#identity","@type":"Organization","alternateName":"CBPF","description":"Unidade de pesquisa do Ministério da Ciência, Tecnologia e Inovação dedicada à pesquisa básica em Física, suas aplicações e à formação científica.","email":"web@cbpf.br","legalName":"Centro Brasileiro de Pesquisas Físicas/CBPF","name":"Centro Brasileiro de Pesquisas Físicas","taxID":"04.044.443/0001-35","telephone":"+55-21-2141-7100","url":"https://cbpf.br","address":{"@type":"PostalAddress","streetAddress":"Rua Dr. Xavier Sigaud, 150","addressLocality":"Rio de Janeiro","addressRegion":"RJ","postalCode":"22290-180","addressCountry":"BR"},"logo":{"@id":"https://index.cbpf.br/#logo"},"sameAs":["https://twitter.com/cbpf_mcti"]},{"@id":"https://index.cbpf.br/#logo","@type":"ImageObject","caption":"Centro Brasileiro de Pesquisas Físicas","contentUrl":"https://index.cbpf.br/icon-512x512-light.png","inLanguage":"en-US","url":"https://index.cbpf.br/icon-512x512-light.png"}]} ``` ## Sitemap See the full [sitemap](https://index.cbpf.br/sitemap.md) for all pages.