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arXiv · 1004.0281

The Bekenstein Bound in Asymptotically Free Field Theory

E. Arias·N. F. Svaiter·G. Menezes
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Abstract

For spatially bounded free fields, the Bekenstein bound states that the specific entropy satisfies the inequality $\frac{S}{E} \leq 2 πR$, where $R$ stands for the radius of the smallest sphere that circumscribes the system. The validity of the Bekenstein bound on the specific entropy in the asymptotically free side of the Euclidean $(λ\,ϕ^{\,4})_{d}$ self-interacting scalar field theory is investigated. We consider the system in thermal equilibrium with a reservoir at temperature $β^{\,-1}$ and defined in a compact spatial region without boundaries. Using the effective potential, we presented an exhaustive study of the thermodynamic of the model. For low and high temperatures the system presents a condensate. We obtain also the renormalized mean energy $E$ and entropy $S$ for the system. With these quantities, we shown in which situations the specific entropy satisfies the quantum bound.

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E. Arias, N. F. Svaiter, G. Menezes. 2010-04-02. The Bekenstein Bound in Asymptotically Free Field Theory. https://doi.org/10.1103/physrevd.82.045001

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