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Information-Theoretic Black Hole Entropy I: Beyond the Area Law
Alex Kehagias
https://arxiv.org/abs/2608.05795 https://arxiv.org/pdf/2608.05795 https://arxiv.org/html/2608.05795
arXiv:2608.05795v1 Announce Type: new
Abstract: Although the Bekenstein-Hawking area law is consistent with the first and second laws of black hole thermodynamics, it appears to be in conflict with the third law, which in the Nernst formulation states that the entropy should either vanish or approach a universal constant in the zero-temperature limit. We argue that this tension reflects a limitation of the semiclassical area law rather than a fundamental feature of black hole thermodynamics. On this basis, we obtain an entropy formula that is consistent with the third law, and approaches Bekenstein-Hawking entropy in the high-temperature limit. The resulting entropy admits a simple microscopic interpretation, and it can be written as the Kullback-Leibler divergence between a mass-biased Bernoulli distribution and the uniform distribution on N microscopic bits. From this perspective, the thermodynamic black hole entropy admits an information-theoretic representation as an entropy deficit, namely as the relative entropy between the black hole ensemble and a maximally mixed reference ensemble. The Bekenstein-Hawking area law then emerges as the leading term in an $1/N$ expansion, while a universal mass scale $M_0=\sqrt{N}\,M_P$, interpreted as an absolute upper bound on the black hole mass, controls the bias of the underlying microscopic ensemble. The subleading terms represent finite-information corrections to the classical area law.
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Spectral phase transitions in Gaussian multi-index models
Florent Krzakala, Pierre Mergny, Vanessa Piccolo
https://arxiv.org/abs/2608.12183 https://arxiv.org/pdf/2608.12183 https://arxiv.org/html/2608.12183
arXiv:2608.12183v1 Announce Type: new
Abstract: Recovering a low-dimensional latent subspace from nonlinear observations of Gaussian covariates in high dimensions is a fundamental problem in feature learning. Here, we consider Gaussian multi-index models in which the covariates $\boldsymbol{x}_i \stackrel{\mathrm{i.i.d.}}{\sim} \mathcal{N}(0,\boldsymbol{I}_d)$ and the responses $\boldsymbol{y}_i$ depend on $\boldsymbol{x}_i$ only through its projection onto an unknown $r$-dimensional subspace. Earlier work based on approximate message passing (AMP) identified a sharp threshold for weak recovery [Troiani et al., 2025], raising the question of whether it can be attained, without side information, by a spectral method. We answer this affirmatively and develop a general random matrix theory for matrix-valued spectral estimators of the form \[\boldsymbol{D}_n=\frac{1}{n}\sum_{i=1}^n\boldsymbol{T}(\boldsymbol{y}_i)\otimes\boldsymbol{x}_i\boldsymbol{x}_i^\top,\] where $\boldsymbol{T}$ is an arbitrary bounded symmetric matrix-valued preprocessing map of fixed dimension. As $n,d \to \infty$ with $n/d\to\alpha$, we prove that the empirical spectral measure of $\boldsymbol{D}_n$ converges almost surely to a deterministic compactly supported distribution characterized by a matrix-valued self-consistent equation. We then establish a spectral phase transition for the largest eigenvalue: below threshold it sticks to the bulk edge, while above threshold an outlier emerges. We characterize the outlier location through a finite-dimensional deterministic equation and show that the associated spectral estimator achieves weak recovery of the latent subspace. Finally, we prove that the AMP-derived preprocessing of [Defilippis et al., 2025] is optimal among all bounded matrix-valued preprocessing maps of any fixed dimension. Its transition coincides with the AMP weak-recovery threshold, proving the general spectral conjecture of [Defilippis et al., 2025].
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Universal scaling of electrochemical information transfer at solid-liquid interfaces
Eikichi Kimura, Ashutosh Rathi, Saki Tsuchiya, El Mustapha Mansouri, Sara Mandi\'{c}, Kristi Kanya Saikia, Keisuke Oshimi, Masazumi Fujiwara, Keigo Arai
https://arxiv.org/abs/2607.22190 https://arxiv.org/pdf/2607.22190 https://arxiv.org/html/2607.22190
arXiv:2607.22190v1 Announce Type: new
Abstract: Electrochemical potentials at solid-liquid interfaces govern diverse chemical and energy conversion processes; however, the extent to which their electrochemical influence extends into the solid remains unclear. This study demonstrates that the maximally accessible electrochemical information is controlled by a single dimensionless factor $u$, defined as the ratio of the effective electrostatic separation between the liquid and probe locations to the electrostatic propagation length in the solid. The resulting universal inverse-square scaling is independent of the microscopic details of the probe. This attenuation law identifies electrostatic screening as a fundamental constraint on information transfer across solid-liquid interfaces, providing quantitative design principles for subsurface electrochemical sensing.
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"By taking advantage of this flaw ... researchers were able to make popular LLMs spit out information they had been trained not to provide, such as how to synthesize cocaine and how to sabotage a commercial aircraft's navigation system. "There's a real probability that this is going to be a problem that's fundamentally unsolvable"
A Fundamental Flaw Leaves LLMs Strikingly Vulnerable To Attack - Slashdot
https://slashdot.org/story/26/07/30/2037233/a-fundamental-flaw-leaves-llms-strikingly-vulnerable-to-attack