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Strominger–Thompson Quantum Bousso Bound

Prove that for any quantum lightsheet L_qu(γ1, γ2) in semiclassical gravity, the coarse-grained (thermodynamic) entropy S_th(L_qu(γ1,γ2)) is bounded by the difference of quantum areas, i.e., S_th(L_qu(γ1,γ2)) ≤ (Area_qu(γ1) − Area_qu(γ2))/(4G).

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Background

The classical Bousso bound uses area differences and relies on the NEC; quantum effects motivate replacing area by generalized (quantum) area. Strominger and Thompson conjectured a quantum version bounding the coarse-grained entropy flux on a quantum lightsheet by quantum area differences. The thesis proves this bound in JT gravity under hydrodynamic assumptions.

References

Conjecture [Strominger-Thompson quantum Bousso bound] Let $\mathcal{L}{\rm qu}(\gamma_1,\gamma_2)$ be a quantum lightsheet that emanates and terminates orthogonally from two codimension-two spacelike hypersurfaces $\gamma_1$ and $\gamma_2$. Then, \begin{equation} \label{eq:STBB} S{\rm th}(\mathcal{L}{\rm qu}(\gamma_1,\gamma_2)) \leq \frac{\text{Area}{\rm qu}(\gamma_1)-\text{Area}{\rm qu}(\gamma_2)}{4G}, \end{equation} where $S{\rm th}(\mathcal{L}_{\rm qu}(\gamma_1,\gamma_2))$ is the thermodynamic entropy of the lightsheet.

— Information-theoretic constraints in quantum gravity and cosmology (2510.15787 - Franken, 17 Oct 2025) in Chapter: Entropy and energy bounds in semiclassical gravity, Section: Quantum Bousso Bounds