Quantum Bound on the Specific Entropy in Strong-Coupled Scalar Field Theory
| dc.creator | Alcalde, M. Aparicio | |
| dc.creator | Menezes, G. | |
| dc.creator | Svaiter, N. F. | |
| dc.date | 2007-11-21 | |
| dc.date | 2008-06-03 | |
| dc.date.accessioned | 2026-07-07T11:38:51Z | |
| dc.date.available | 2026-07-07T11:38:51Z | |
| dc.description | Using the Euclidean path integral approach with functional methods, we discuss the $(g_{0} ϕ^{p})_{d}$ 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 $β^{-1}$. For spatially bounded free fields, the Bekenstein bound states that the specific entropy satisfies the inequality $\frac{S}{E} < 2 πR$, 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 $ε_d^{(r)}$ as the renormalized zero-point energy for the free theory per unit length, the dimensionless quantity $ξ=\fracβ{L}$ 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 $\frac{S}{E} < 2πR \frac{h_1(d)}{h_2(d)} ξ$. When considering the low temperature behavior of the specific entropy, we have $\frac{S}{E} <2πR \frac{h_1(d)}{ε_d^{(r)}}ξ^{1-d}$. 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. | |
| dc.description | Accepted for publication in Physical Review D | |
| dc.identifier | https://arxiv.org/abs/0711.3435 | |
| dc.identifier | http://arxiv.org/abs/0711.3435 | |
| dc.identifier | Phys.Rev.D77:125024,2008 | |
| dc.identifier | doi:10.1103/PhysRevD.77.125024 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/199715 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Quantum Bound on the Specific Entropy in Strong-Coupled Scalar Field Theory | |
| dc.type | text |