The Bekenstein Bound in Asymptotically Free Field Theory

Abstract

For spatially bounded free fields, the Bekenstein bound states that the specific entropy satisfies the inequality $\frac{S}{E}\le 2\pi R$, 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 $(\lambda {\varphi }^4{)}_d$ self-interacting scalar field theory is investigated. We consider the system in thermal equilibrium with a reservoir at temperature ${\beta }^{-1}$ 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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• The holographic principle
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Cited by in corpus (1)

• Scalar Quantum Field Theory in Disordered Media