Quantum Bound on the Specific Entropy in Strong-Coupled Scalar Field Theory

Abstract

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 ${\epsilon }_d^{(r)}$ 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 $\frac{S}{E}<2\pi R\frac{h_1(d)}{{\epsilon }_d^{(r)}}{\xi }^{1-d}$. 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.

Accepted for publication in Physical Review D

References in corpus (25)

• New Developments in the Casimir Effect
• Zeta Functions and the Casimir Energy
• Entropy Bounds and Black Hole Remnants
• Heat-kernel coefficients of the Laplace operator on the D-dimensional ball
• Casimir energies for massive fields in the bag
• On the ground state energy for a penetrable sphere and for a dielectric ball
• Quantum Limitations on the Storage and Transmission of Information
• How does the entropy/information bound work ?
• Vacuum Energy Density near Fluctuating Boundaries
• Zero-point energy of massless scalar fields in the presence of soft and semihard boundaries in D dimensions
• Casimir Energy of Massless Fermions in the Slab-bag
• Casimir energy of a massive field in a genus-1 surface
• One-Loop Renormalization of a Self-Interacting Scalar Field in Nonsimply Connected Spacetimes
• Finite Size Effects in the Anisotropic λ/4!(ϕ^4_1 + ϕ^4_2)_d Model
• Effective Lagrangians for Scalar Fields and Finite Size Effects in Field Theory
• Entropy Bounds in $R\times S^3$ Geometries
• The Two-loop Massless phi^4 Model in Non-translational Invariant Domain
• Finite Size Effects in Thermal Field Theory
• Bound states and the Bekenstein bound
• Zero modes, entropy bounds and partition functions
• The thermal energy of a scalar field in a one-dimensional compact space
• Attractive Casimir effect in an infrared modified gluon bag model
• Note on Bound States and the Bekenstein Bound
• Bekenstein Bound and Spectral Geometry
• The Partition Function for the Anharmonic Oscillator in the Strong-Coupling Regime

Cited by in corpus (1)

• The Bekenstein Bound in Asymptotically Free Field Theory