Wu et al. (arXiv:2610.35790) introduced entropy imaging for quantum matter: a microscopy image is serialized along a Hilbert curve, compressed with a lossless algorithm, and the computable information density (CID) is used as a measure of spatial complexity. Applied to microwave impedance microscopy of graphene, CID peaks near quantum Hall transitions, tracks fractional transitions, and resolves fractional puddles in a local map, while a trivial band-edge crossover does not show the same enhancement. This preprint offers an information-dynamics reading of that result. In this reading, a microscopy image is a projection, and CID is treated as an indicator of the arrangement information in the projection. The reading changes no number in Wu et al. No new data are reported. All numbers are Wu et al.'s as reported. Three falsifiable predictions are stated, testing the CID diagnostic.
Wu et al. (arXiv:2610.35790) introduced entropy imaging for quantum matter: a microscopy image is serialized along a Hilbert curve, compressed with a lossless algorithm, and the computable information density (CID) is used as a measure of spatial complexity. Applied to microwave impedance microscopy of graphene, CID peaks near quantum Hall transitions, tracks fractional transitions, and resolves fractional puddles in a local map, while a trivial band-edge crossover does not show the same enhancement. This preprint offers an information-dynamics reading of that result. In this reading, a microscopy image is a projection, and CID is treated as an indicator of the arrangement information in the projection. The reading changes no number in Wu et al. No new data are reported. All numbers are Wu et al.'s as reported. Three falsifiable predictions are stated, testing the CID diagnostic.
Phase transitions can generate intricate spatial organization invisible to spatially averaged probes, yet quantitative measures of this organization remain limited. Here we develop "entropy imaging," an information-theoretic technique that harnesses lossless compression to quantify spatial complexity, predictability, and order in quantum materials. Using this approach, emergent spatial textures can be imaged and converted into an experimentally-accessible observable: the computable information density (CID), a compression-based measure of information complexity that approaches the Shannon entropy rate in the large-system limit. Applied to millikelvin microwave impedance microscopy of graphene, the method reveals a pronounced maximum in the CID near quantum Hall transitions, a quantitative measure of the information-rich spatial organization of the critical landscape. A disordered Hofstadter model reproduces this behavior and shows that the CID can identify the quantum critical point from a sequence of images, without ensemble averaging over disorder realizations. The same framework tracks fractional quantum Hall transitions and resolves isolated fractional puddles that coexist with a disordered background. By contrast, the trivial band-edge crossover in a MoSe2/WS2 moiré heterobilayer exhibits qualitatively different behavior, suggesting that the pronounced CID enhancement observed at the quantum Hall critical point is not simply a generic feature of a conductive-insulating crossover. We further show that the geometric information encoded in CID is not reducible to a correlation length, and it can even distinguish spatial textures with identical multifractal statistics. Together, these results establish lossless compression as a framework for quantifying emergent spatial organization in quantum materials, with portability across imaging modalities and physical systems.
The outcomes of projective measurements on a quantum many-body system in a chosen basis are inherently probabilistic. The Shannon entropy of this probability distribution (the "diagonal entropy") often reveals universal features, such as the existence of a quantum phase transition. A brute-force tomographic approach to estimating this entropy scales exponentially with the system size. Here, we explore using the Lempel-Ziv lossless image compression algorithm as an efficient, scalable alternative, readily implementable in a quantum gas microscope or programmable quantum devices. We test this approach on several examples: one-dimensional quantum Ising model, and two-dimensional states that display conventional symmetry breaking due to quantum fluctuations, or strong-to-weak symmetry-breaking due to local decoherence. We also employ the diagonal mixed state to put constraints on the phase boundaries of our models. In all examples, the compression method accurately recovers the entropy density while requiring at most polynomially many images. We also analyze the singular part of the diagonal entropy density using renormalization group on a replicated action. In the 1+1-D quantum Ising model, we find that it scales as ∣t∣log∣t∣, where t is the deviation from the critical point, while in a 2+1-D state with amplitudes proportional to the Boltzmann weight of the 2D Ising model, it follows a t2log∣t∣ scaling.
The concept of entropy is central to both classical thermodynamics and quantum information science. In conventional treatments, entropy is a scalar quantity associated with a statistical ensemble or a quantum state. This paper introduces a novel perspective in which quantum systems support an entropy flow field, denoted J_S(x,t), analogous to the heat current in classical thermodynamics. We develop a rigorous theoretical framework for defining and calculating entropy flow in closed and open quantum systems, and we propose a method for imaging this flow by mapping local entropy production rates onto spatial coordinates. The resulting Quantum Entropy Flow Imaging (QEFI) technique offers a powerful diagnostic tool for probing nonequilibrium quantum dynamics, revealing hidden structure in entanglement propagation, and bridging the gap between quantum information and thermodynamic concepts. While the experimental implementation of QEFI is left for future work, we outline how quantum simulators and ultracold atomic gases can be employed to test the predictions. The potential to observe entropy currents in quantum devices opens new avenues for exploring fundamental questions about the nature of entropy, information flow, and their role in quantum technologies.
Computable information density (CID), the ratio of the length of a losslessly compressed data file to that of the uncompressed file, is a measure of order and correlation in both equilibrium and nonequilibrium systems. Here we show that correlation lengths can be obtained by decimation, thinning a configuration by sampling data at increasing intervals and recalculating the CID. When the sampling interval is larger than the system's correlation length, the data becomes incompressible. The correlation length and its critical exponents are thus accessible with no a priori knowledge of an order parameter or even the nature of the ordering. The correlation length measured in this way agrees well with that computed from the decay of two-point correlation functions g_{2}(r) when they exist. But the CID reveals the correlation length and its scaling even when g_{2}(r) has no structure, as we demonstrate by "cloaking" the data with a Rudin-Shapiro sequence.
Entanglement entropy is a useful probe of compressible quantum matter because it can detect the existence of Fermi surfaces, both of microscopic fermionic degrees of freedom and of ``hidden'' gauge-charged fermions. Much recent attention has focused on holographic efforts to model strongly interacting compressible matter of interest for condensed matter physics. We complete the entanglement analysis initiated by Huijse et al. [Phys. Rev. B 85, 035121 (2012)] and Ogawa et al. [JHEP 1 (2012) 125] using the recent proposal of Faulkner et al. (arXiv:1307.2892) to analyze the entanglement entropy of the visible fermions which arises from bulk loop corrections. We find perfect agreement between holographic and field-theoretic calculations.
A recurring pattern in the recent quant-ph, math-ph, math.QA, and cond-mat.stat-mech preprints — read over a thirty-day window ending 2026-06-02 — suggests that several structures long treated as primary coordinates of many-body Hilbert space are in fact derived. Entanglement magnitude, the existence of a free-fermion language, dynamical universality classes, the ground-state manifold, and even the complex-versus-real structure of the operator algebra each appear, in independent recent work, to refine into finer distinctions once one asks two prior questions: *how is locality measured?* and *which symmetry resolves the count?* We collect seven specific findings — Gheorghiu's constant-depth pseudoentanglement separation [corpus:arxiv:2605.31448v1], Lu, Fu and Liu's intrinsic-locality dimension for stabilizer codes [corpus:arxiv:2605.31441v1], Jindal and Hosur's non-Abelian-ETH entropy correction [corpus:arxiv:2605.30798v1], Fukai, Pozsgay and Vona's path-product expansion for hidden free fermions [corpus:arxiv:2605.31453v1], Sinha and collaborators' hidden Ising structure from a generalized Yang-Baxter equation [corpus:arxiv:2605.30007v1], Balducci and collaborators' traversable-versus-nontraversable quantum phase transitions [corpus:arxiv:2605.31472v1], and Surace, Minagawa and Kunjwal's reversal of the real-complex hierarchy under indefinite causal order [corpus:arxiv:2605.30238v1]. We also use Divi, Lessa and Wang's local strong-to-weak SSB diagnostic [corpus:arxiv:2605.28967v1] as an internal cross-check. The thesis we synthesize: *the apparent dimensionality, universality, and even reality of a quantum system are conditional on the choice of locality metric and the symmetry resolution applied to its Hilbert space; they are not intrinsic features of the state or Hamiltonian alone.* The falsification path: each refinement we cite is operationally testable — a constructed example, a closed-form bound, or a finite-data diagnostic — and the thesis fails if any of the underlying mechanisms is retracted, or if a counter-example emerges in which a symmetry resolution or locality metric does not change the structural conclusion. The contribution here is the synthesis, not the underlying results. Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted from arXiv preprint corpus on the date in the filename. Cited arXiv preprints: 2605.28967v1, 2605.30007v1, 2605.30238v1, 2605.30798v1, 2605.31441v1, 2605.31448v1, 2605.31453v1, 2605.31472v1