Papers

Chiral active fluids, composed of continuously rotating active constituents, exhibit a wealth of nonequilibrium phenomena arising from the interplay of activity, hydrodynamic interactions, and broken mirror symmetry. While these systems naturally generate circulating flows and active turbulence, converting their microscopic rotational motion into directed macroscopic transport remains an open challenge. By means of mesoscale hydrodynamic simulations, here we show that channels with an intrinsic asymmetry result in the spontaneous formation of a persistent net flux in the absence of externally imposed pressure gradients or body forces. Our results can be extrapolated to various geometric confinement strategies providing efficient and versatile strategies for transforming chiral activity into autonomous fluid transport, such that they can be utilized as a promising platform for self-powered microfluidic pumping.

A single-molecule experiment on a driven enzyme or motor resolves only a few of the transitions the machine makes, yet one would like to know how much free energy it dissipates in total, including on the steps that stay hidden. The mean and the fluctuations of the currents on the watched transitions are shown to certify this hidden dissipation, with no knowledge of the transition rates and no access to the hidden transitions: when the watched transitions span the cycles of the network, the observed-current covariance recovers the full density-contracted quadratic current geometry, including the contribution of transitions that are never seen. The mechanism is that fluctuations are set by the dynamical activity, or traffic, the symmetric partner of the current. Contracting the large-deviation cost of empirical currents over density fluctuations identifies the observed-current covariance with a traffic-weighted metric, and turns partial observation into a minimum-energy completion problem over the unseen cycles, whose solution is the certified hidden cost. Existing current-fluctuation uncertainty relations bound dissipation from chosen currents but do not say when partial observation fixes the hidden contribution; the cycle-observability condition derived here does. The statements concern long-time means and fluctuations; finite-time estimates require separate error control.

We study the two-dimensional XY model with the nonanalytic pair potential $2[(1-\cos\delta)/2]^{p}$, whose small-angle law $\propto|\delta|^{2p}$ carries a cusp for $p<1$ and a flat bottom for $p>1$, invalidating the harmonic spin-wave expansion. Two questions arise: the nature of the low-temperature ($T$) phase and of the phase transition. A naive energetic argument would predict genuine long-range order and an enhanced transition temperature for $p<1$, and no transition at all for $p>1$. Large-scale Monte Carlo simulations contradict both: for every $p>0$ the \dengrevxxi{low-$T$ phase} is quasi-long-range ordered, with anomalous dimension $\eta(T)\propto T^{1/p}$, and terminates at a Berezinskii–Kosterlitz–Thouless transition. Using a vortex-free noncompact lattice-field description and utilizing a duality transformation, we show that coarse-graining drives the height-difference distribution onto a single Gaussian fixed point, renormalizing the cusp and flatness into a finite harmonic stiffness that restores the spin-wave description and the BKT scenario for all $p>0$.

Charge transport in solid-state materials is often governed by charge carrier hopping processes in the presence of long-range electrostatic interactions. Kinetic Monte Carlo (kMC) simulations provide a framework for describing such rare-event dynamics over extended timescales. However, the efficient treatment of long-range interactions remains a major computational challenge, since each particle jump modifies the energy landscape globally and, in principle, requires updating all transition rates after every carrier motion. We present an efficient and generally applicable update process for these transition rates in the presence of long-range electrostatic interactions. To illustrate the method, we study charge diffusion on a simple cubic host lattice under an external electric field. The transport behavior is investigated in high states of charge (SOC), and the influence of temperature, electric field strength, and SOC is examined. Our simulations show strongly suppressed transport at 100\,% SOC (50\,% occupation) caused by a freezing of the charge carriers into a Coulomb superlattice. Slight deviations from this reference in terms of charge carrier concentration lead to a rapid increase in conductivity. A deeper analysis reveals that this behavior can be rationalized as transport of non-interacting defects in the Coulomb superlattice. These results demonstrate the capability of the proposed update procedure to efficiently capture non-equilibrium transport phenomena in interacting charged systems and provide a foundation for simulations of more complex charge diffusion problems.

We derive thermodynamic speed limits for isolated quantum systems undergoing finite-time unitary driving. The key ingredient is a set of generalized second-law inequalities: for the Gibbs entropy and for several thermodynamically motivated observational entropies, the entropy production is bounded from below by a function of the Vu–Saito quantum Wasserstein distance between the initial and final coarse-grained states. These inequalities yield lower bounds on the operation time in terms of the average entropy-production rate. We apply the framework to system–bath coarse-graining, local-energy coarse-graining, and diagonal entropy, and illustrate the resulting bounds with numerical and analytically solvable examples. Our results provide a thermodynamic characterization of finite-time state transformations in isolated quantum systems and clarify how coarse-grained entropy production constrains macroscopic reachability.

We propose a tensor-network Monte Carlo (TNMC) approach for unitary evolution following the compression sequence of the time-evolving block decimation (TEBD) algorithm. In the TNMC approach, the obtained results contain evaluable statistical errors rather than truncation errors, unlike ordinary singular-value-decomposition-based methods such as the TEBD algorithm. Consequently, one can estimate unbiased expectation values within statistical errors even with a finite bond dimension. Since the sampling scheme is introduced in the simulations of unitary evolution, the proposed Monte Carlo scheme may suffer from a sign problem. We observe that the sign problem can be mitigated by increasing the bond dimension. We apply the proposed TNMC approach to the Hamiltonian and the Floquet dynamics. Numerical experiments show that the TNMC approach can estimate accurate expectation values of observables even when the TEBD method with the same bond dimension cannot. The proposed approach can be a new direction for improving the classical simulatability of unitary evolution.

Self-organisation of granular systems is a key determinant of their macroscopic behaviour and has been studied extensively in assemblies of hard particles. We use numerical simulations to test this understanding in mixtures of hard and soft particles, focusing on cells, the smallest irreducible loops of the contact network, as structural descriptors. We show that, while the cell statistics display robust qualitative features under isotropic compaction, they depend on inter-particle friction, $\mu$, and soft-particle fraction, $\kappa$. Specifically, (i) the quadron area distributions retain a $\Gamma$ form, albeit with parameters that vary systematically with $\mu$ and $\kappa$. (ii) Predictions of the cell order distribution (COD) by maximising the entropy, without taking mechanical stability into consideration, become increasingly inaccurate at large cell orders. (iii) Irrespective of $\mu$, the normalised cell stress distributions collapse onto one master Weibull form, whose only shape parameter depends weakly on $\kappa$. This suggests a quasi-universal form that may deteriorate slightly at very high fractions of soft particles. (iv) Cells align preferentially along the local major principal stress direction, showing the same coordinated stress–structure self-organisation as in hard particles. The relative robustness of cell statistics to the addition of soft particles suggests that hard and hard–soft granular mixtures can be described by one model.

We study the notion of temperature in uniformly accelerated frames within a relativistic thermodynamic framework. Considering a perfect fluid at rest in a non-inertial (Rindler) frame, we derive the condition for thermal equilibrium from energy–momentum conservation. This leads to a position-dependent temperature profile consistent with the Tolman–Ehrenfest relation. We emphasize that this temperature characterizes the local thermodynamic equilibrium of the fluid in the accelerated frame and does not arise from a transformation law between different observers. The physical interpretation of the result and its relation to acceleration-induced effects are briefly discussed.

The breaking or fracture of materials and damages or devastations due to earthquakes have caught our attention since the earliest stage of human civilization. In fact, at around 1500, Leonardo Da Vinci made the pioneering observation that, unlike elastic constants (formalized later by Hooke in 1678) of the materials, the tensile (breaking) strengths of nominally identical iron wires decrease drastically with their length, indicating the vanishing breaking strength of materials in the large size limit, suggesting the impossibility of constructing arbitrarily large structures. This was the first observation that unlike the elasticity of disordered materials, which remains defined in the thermodynamic limit (self averaging statistics), the breaking properties of the disordered materials have extreme (non self averaging) statistics. In spite of major and some precise developments in statistical physical modelling and characterizing the fracture mechanics (starting with Allan Griffith's crack nucleation theory in 1921 and the weakest link failure Fibre Bundle Model of Frederick Thomas Peirce in 1926) and of earthquake dynamics (starting with Robert Burridge and Leon Knopoff's continuum dynamical model in 1967 and later other discrete or lattice train models or fractal overlap models of stick slip earthquakes), no graduate level textbook in condensed matter physics or in statistical physics introduces the basic models and their properties. And now computer scientists and social scientists (coming with their social inequality measures applied to the avalanche statistics in precursor failures) are joining their efforts to explore the new precursory inequality measures for big avalanches or failures. This introductory review is designed to fill this gap with a view to introducing these to this wider audience and to take them to the current frontiers in these fields.

We find a striking departure from simple electrostatics in a family of two-dimensional lattice models whose effective description takes the form of an emergent electromagnetism: a high-order multipolar charge configuration can induce an electric field characteristic of a lower-order multipole. Studying the archetypical hardcore dimer and U(1) spin-1/2 link models, we trace this to a breakdown of the superposition principle: for dense charge configurations, there can be a nonlinear suppression, or even enhancement, of the far field compared to the linear expectation. Our work establishes that microscopic lattice-scale constraints in models for emergent electromagnetism can change the far-field behaviour to differ from often utilized long-wavelength descriptions in standard effective continuum models.

Modern effective field theories of dissipative hydrodynamics, built on the Schwinger-Keldysh (SK) formalism, include thermal noise that is not Gaussian. The resultant higher-order noise vertices are constrained by symmetries, but otherwise treated as free parameters. We show explicitly that symmetry constraints alone do not guarantee these vertices yield a genuine probability distribution. Requiring a probability interpretation yields sharp bounds between cumulants that are invisible to the symmetry analysis. The bounds are optimal: their boundaries are attained by explicit positive distributions, and constructive completions are provided for both negative- and positive-kurtosis noise data. This gives closed-form nonlinear response and an exact sampling algorithm, whose Monte Carlo implementation reproduces the exact cumulants and nonlinear fluctuation-dissipation relations. Confronted with microscopic results, the framework places a sharp lower bound on the time step required for a positive stochastic completion of a quartic model of the Brownian particle used in the literature, while holographically computed $SU(2)$ noise vertices pass a nontrivial continuum fourth-order positivity test.

We compute mutual information for general spacetime regions using Sorkin's Gaussian field formalism. We show that this construction is naturally based on the reduced space of smearings that generate independent fields, making manifest that in QFTs with stress tensor the local algebras generated by regions sharing the same causal completion. We test the method for a Weyl fermion, the chiral current, and massless and massive real scalar fields across various spacetime regions in 1+1 Minkowski space. Across all cases, distinct spacelike-separated spacetime regions sharing the same causal completion yield identical mutual information. This formalism provides a setting in which to test the timelike tube theorem. Indeed, we observe that the mutual information of a timelike lens approaches that of its enveloping diamond as the cutoff is increased, offering a direct numerical verification of the theorem. In all the considered cases, our results agree with known continuum and spatial-lattice results. Finally, this work establishes a natural framework for studying entanglement measures in generalized free field theories, a task that is impractical within other existing prescriptions.

Rényi coherent information, a computable proxy for the von Neumann coherent information, is widely used to study mixed-state phases of matter and decodability transitions in noisy quantum error-correcting codes. However, being a difference of two Rényi entropies, it need not be monotonic in the Rényi index, and lacks the operational meaning of its von Neumann counterpart. Here we address both issues for stabilizer codes. First, for Pauli noise generated by independent Bernoulli events, we prove that the Rényi-$n$ coherent information is nondecreasing in $n \in \mathbb{Z}^+$. This follows from a general theorem: if independent random bits are mapped linearly to a fine label $T$ and a coarse label $C$, then the Rényi entropy difference $H_n(C)-H_n(T)$ is nondecreasing in $n$. For stabilizer codes, $T$ is the joint syndrome–logical class and $C$ is the syndrome, and the difference is the Rényi-$n$ coherent information up to a constant. The same theorem covers classical linear codes and independent detector error models. Second, for arbitrary stochastic Pauli noise, we give the Rényi-$n$ coherent information an operational meaning via postselection on matching syndromes between one data block and $n-1$ auxiliary blocks. We determine when this defines a quantum channel and show that saturation of the Rényi-$n$ coherent information is equivalent to asymptotically perfect recovery of the postselected channel. Moreover, the Rényi-$n$ coherent information also upper-bounds the ordinary coherent information achievable after any syndrome-conditioned recovery.

Quantifying properties of quantum states through the limits of their manipulation is a central goal of quantum resource theories. For symmetry breaking, the quantum geometric tensor (QGT) governs asymptotic pure-state conversion, but a complete characterization for general mixed states has remained elusive. Here we fully resolve this problem for finite-dimensional systems under compact Lie group symmetries in the i.i.d. asymptotic regime. Specifically, we establish a single-letter formula for the optimal conversion rate between arbitrary states, with vanishing trace-distance error, in the resource theory of asymmetry. The rate is determined by a one-parameter family of metric adjusted QGTs, obtained by rescaling quantum Fisher information (QFI) matrices that interpolate between the symmetric logarithmic derivative and right logarithmic derivative (RLD) QFIs. For pure states, the RLD endpoint recovers the standard QGT. No state-independent finite subset of this family suffices in general, even for $U(1)$ symmetry, revealing a qualitative distinction from pure-state conversion. Our formula further yields an exact pure-state distillation-rate formula in terms of a single asymmetry measure, characterizes asymptotically reversible interconversion, and identifies bound asymmetry for quantum clocks. Complementarity among members of the metric adjusted QGT family also reveals an activation mechanism: a state with zero conversion rate to a mixed clock state can still enhance another input's yield under joint processing. Our proof relies on two developments of independent interest. First, we extend quantum local asymptotic normality to unitary models with arbitrary rank and spectral degeneracy. Second, we characterize convertibility between quantum Gaussian shift models in terms of the same one-parameter family of QFIs.

We introduce a systematic block entropy area based mode optimization algorithm for many-body quantum states of interacting fermions represented by matrix product states. From the gradient of a global cost function, the block entropy area, a long-ranged, non-interacting effective disentangler Hamiltonian is formed. We then simulate the time-dependent Schrödinger equation driven by the disentangler Hamiltonian by employing the time-dependent variational principle based on projector splitting, and minimize the cost function. The combination of the density matrix renormalization group with this gradient-based entanglement minimization forms an efficient low-rank iterative ground-state algorithm that also provides an optimized single-particle basis for matrix product state representation. We demonstrate the method on two-dimensional lattice models of interacting fermions and the Fe${_4}$S${_4}$ cluster, and show its robustness and superiority over earlier protocols using nearest-neighbor mode rotations and reorderings.

Fuzzy-sphere regularization gives numerical access to three-dimensional conformal field theories (CFTs), but locating one requires testing for criticality across the parameter space of microscopic couplings. We reduce the search cost by about two orders of magnitude, combining an exact diagonalization based on states having definite total angular momentum with a certified reduced-basis emulator that reconstructs energies, observables and their derivatives continuously across the couplings from a handful of exact solutions per system size. The combination reproduces the published ground-state-energy analysis of the fuzzy-sphere Ising model and the published conformal data of a three-flavor fuzzy-sphere realization of the O(2) Wilson–Fisher CFT, including quantities defined by parameter derivatives. Applied to the O(2) model with no CFT input, the ground-state-energy criterion locates the critical coupling to within half a percent of a density matrix renormalization group value obtained on systems more than twice the size, and maps the critical line of the model across the coupling plane. Ground-state criteria locate the critical line robustly, but the point they select along it is weakly determined, and the computed dimensions come closest to the bootstrap elsewhere along the line.

We use evolutionary reinforcement learning to determine efficient time-dependent erasure protocols for an underdamped cantilever moving in a double-well potential, an experimental realization of a 1-bit memory. We investigate how the mean work $\langle W \rangle $ needed to erase a bit scales as a function of the protocol duration $\tau$. We find two regimes, depending on how $\tau$ compares to the relaxation time of the system $t_r$. For $\tau \gg t_r$, the quasistatic isothermal regime, we recover Landauer's bound plus an overhead that scales as $1/\tau$, similar to the overdamped case. By contrast, for $\tau<t_r$ erasure becomes adiabatic and $\langle W \rangle$ grows more slowly than in the isothermal case. This growth is bounded from below as $1/\tau$, which we derive using a gedanken optimal protocol. Finally, comparison with overdamped erasure shows that learned protocols can outperform protocols that are optimal subject to equilibrium boundary conditions.

We construct the first fully spatially local fault-tolerant quantum computer based on topological codes in fewer than four spatial dimensions. Our construction is a two-dimensional architecture that uses only geometrically local quantum and classical operations, bounded-speed classical communication and computation, and a constant density of quantum and classical resources. The core component is a new time-translation-invariant cellular-automaton decoder for the surface code. This decoder preserves logical information for a time stretched-exponential in the code distance and operates continuously during state injection, stabilizer-state preparation, lattice surgery, and transversal readout. We also prove that every translation-invariant topological Pauli stabilizer code is locally decodable under phenomenological noise.

We study current fluctuations in a temporally random integrable quantum circuit. Commutativity reduces every drive history exactly to its layer composition, turning annealed fluctuations into a competition between current gain and the large-deviation cost of rare compositions. For each fixed composition, homogeneous thermodynamic Bethe ansatz dressing supplemented by ballistic fluctuation theory yields the conditional current statistics. Their annealed large-deviation contraction predicts a first-order switch between two dominant history classes, terminating on a line of regular cusp endpoints. Finite-time analysis shows how the switch is rounded. Thus temporal randomness can act as an emergent order-parameter-like coordinate in trajectory space.

One-dimensional fluids of classical hard-core particles of diameter $a$, interacting in pairs via a soft repulsive (monotonically decreasing) potential of finite range $\varphi(x)=\varepsilon \left[ (a'-x)/(a'-a)\right]^{1/\nu}$ $(a\le x\le a')$ with real positive parameters $\varepsilon$ and $\nu$, are studied in an isothermal-isobaric ensemble. If $a'\le 2a$, the pairwise interactions are reduced to nearest-neighbour interactions, which allows for an exact solution of the thermal equilibrium. We focus on the $T\to 0$ ground states, specifically on the equation of state for the mean distance between nearest neighbours $l_0$ and the pair correlation function $g_0(x)$. If $\varphi(x)$ is concave $(\nu\ge 1)$, there exists an “incompressibility” pressure $p_i=\varepsilon/(a'-a)$ such that the ground state is an equidistant chain of particles with spacing $l_0=a'$ for $0<p<p_i$ and with spacing $l_0=a$ for $p>p_i$. If $\nu>1$ (strict concavity), the ground state at $p=p_i$ is disordered with $l_0=\left[ \nu a +(\nu-1)a'\right]/(2\nu-1)$ and $g_0(x)$ being a superposition of weighted Dirac delta functions over discrete positions. If $\nu=1$ (linear ramp), the ground state at $p=p_i$ is disordered with $l_0=(a+a')/2$ and the continuous $g_0(x)$ is a superposition of Heaviside step functions multiplied by polynomials in $x$. The isothermal susceptibility at $T=0$ is nonzero for concave $\varphi(x)$ ($\nu\ge 1$) at $p=p_i$ and, therefore, the corresponding disordered ground states are non-hyperuniform, i.e., they resemble disordered fluids at nonzero temperatures. It turns out that pair correlation functions of disordered ground states, which occur only at a single pressure $p_i$, extend their predictive power to thermodynamic states at nonzero temperatures over a wider range of pressures around $p_i$.

We study the statistical properties of passive and active many-body systems with orientational degrees of freedom on non-orientable domains. By rephrasing topological constraints as non-local symmetry relations on an orientable double-cover, we show that non-orientability eliminates global rotational soft modes without acting like an external field. In a passive XY model, this results in topological caging, where orientational fluctuations that exhibit conventional diffusive behavior on a torus saturate on a Klein bottle to a finite value that we compute exactly in the thermodynamic limit. In models of active self-propelled particles with orientational degrees of freedom, topological caging persists despite continuously changing interaction neighborhoods. In an active Ising spin model, non-orientability enforces the coexistence of ordered anti-parallel domains with vanishing global polar order, a state that is absent on orientable domains.

Open chemical reaction networks exhibit stochastic concentration dynamics at finite system sizes, whereas their macroscopic limit is governed by deterministic rate equations that can display chaos. In this Letter, we show theoretically that a rate of information loss constructed from two-time mutual information recovers the Kolmogorov-Sinai entropy in the deterministic limit. We verify this result through numerical simulations of a Markov jump process for a three-species system involving seven reactions.

Statistical physics extracts macroscopic laws by averaging over the many microscopic degrees of freedom of a system. Disordered systems demand a second and far harder average, one over the quenched randomness itself. The classic analytical routes, the replica and cavity methods, become uncontrolled outside mean-field or tree-like limits, and conventional numerical algorithms like parallel tempering require expensive, independent equilibration for every disorder realization. In this work, we introduce a universal neural variational framework that amortizes inference across the disorder ensemble, eliminating both the need for per-instance Markov chain equilibration and the cost of retraining instance-specific variational ansatzes. Built on an encoder-decoder Transformer architecture, after training once, it produces an explicit approximation to the Boltzmann distribution given previously unseen disorder realizations without further optimization. We validate this framework on 2D Edwards-Anderson models, and apply it to the random-bond Ising model, successfully capturing the Binder cumulant crossings near the Nishimori multicritical point. These results shift the object of variational inference from the single instance to the disorder ensemble, opening a route to frustrated many-body systems where instance-by-instance computation is prohibitive.

This paper is the second in a two-part investigation of the physics of information geometry. While Part I develops a physical foundation for distributional motion on the probability simplex, the present paper studies how that framework manifests in active inference. The treatment is fully self-contained and does not require familiarity with Part I. We focus in particular on active inference through small distributional steps and the geometric structure induced by such local motion. Starting from an initial distribution, an agent evolves its belief state toward a final target distribution through a sequence of constrained updates. We define a relative free energy functional with respect to the preferred distribution and extend it to a relative potential energy analogous to the Helmholtz/Gibbs free-energy decomposition. The evolution is subject to a per-step kinetic constraint expressed through the Kullback-Leibler (KL) divergence between consecutive distributions, which serves as a discrete kinetic energy on the probability simplex. Using the information-geometric Pythagorean theorem on KL balls, we show that sufficiently small local moves dominate large direct jumps, and that greedy maximization of free-energy reduction is globally optimal under the kinetic constraint. This leads to a sequential variational principle in which the optimal trajectory minimizes the associated Lagrangian of the optimization problem. Similar to classical mechanics, the Lagrangian takes on the form as the difference between the kinetic and potential terms, establishing a least-action principle for distributional motion on the simplex. The resulting optimal update admits a closed form as an exponentially tilted version of the current distribution toward the preferred distribution, parametrized by an inverse-temperature-like multiplier. We further extend the framework to incorporate state-dependent geodesic...

Menshikov and Volkov [Electron. J. Probab. 13 (2008)] studied recurrence and transience of a class of Markovian random walks on $\mathbb R_+$ whose conditional drift depends on both time and position and is of order $\rho x^\alpha t^{-\beta}$ with $\rho>0$. The case on the critical line $2\beta-\alpha=1$, with $\alpha\in(-1,1)\setminus\{0\}$, remained open. We prove recurrence in this remaining case. Furthermore, we establish recurrence and transience criteria that complete the classification for $-1<\alpha<1$ and $\beta\ge 0$, without assuming the Markov property and under weaker assumptions on the increments than those imposed by Menshikov and Volkov.

We investigate timelike entanglement in quantum field theory using spacetime density matrices and provide a microscopic lattice realization. For a two-dimensional free real scalar field, we extend Gaussian diagonalization methods to the generally non-Hermitian reduced spacetime density matrix and determine its complete nonzero spectrum in the generic regular case, together with all integer Rényi moments. The real-time replica construction identifies these moments with Lorentzian branch-point twist-operator correlation functions. We test this identification against the full four-point function on a circle, boundary two-point functions with Dirichlet and Neumann boundary conditions, and massive form-factor predictions, finding quantitative agreement in both magnitude and phase across distinct causal regimes. The boundary setup exhibits a finite causally connected window in which every integer Rényi entropy is real, showing that reality is not equivalent to causal disconnection. These results provide a microscopic lattice foundation for timelike entanglement and for Lorentzian twist-operator methods beyond equal-time regions.

We perform a numerical study of uniform meandric systems via their encoding by pairs of simple random walks and their interpretation as a model of critical percolation on random planar maps. We investigate certain natural box-crossing events and provide numerical evidence for a strong negative association between opposite open crossings and formulate conjectures on their asymptotic behavior. Our second contribution is a simple law-preserving dynamics on meandric systems, by local peak/valley flips in the walk encoding. Our simulations suggest that the percolation structure decorrelates much faster than the underlying random planar map.

Nonergodic features of chaotic quantum many-body systems are commonly characterized through local observables, fidelity, and entanglement entropy. Here, using global and nonlocal measures of nonstabilizerness (magic), we study quantum many-body scars near infinite temperature in $(1+1)$-dimensional Abelian $\mathbb{Z}_2$ and U$(1)$ lattice gauge theories, both analytically and numerically. We derive an exact closed-form expression for the nonlocal trace distance magic solely from the Schmidt spectrum, reducing the optimization over local unitaries to a finite maximization over stabilizer-compatible Schmidt ranks. We find that scar eigenstates can exhibit extensive global magic despite their anomalously low entanglement, while retaining anomalously large nonlocal magic compared with ergodic states. We further show that constrained Hilbert spaces can generate irreducible nonlocal magic through stabilizer-incompatible Schmidt ranks, even for a flat entanglement spectrum.

Granular slip forecasting can conflate material state, loading progress, and the geometry of event-centered sampling. We separated these contributions in slowly sheared two-dimensional frictional disks using a compact neural score of stress, pressure, coordination, non-affine motion, and force-network observables. The model was developed on 36 trajectories and frozen efore testing on 18 new trajectories under two nested stress-drop definitions. Inspection of held-out results revealed post-event sampling asymmetry; recovery-aware analyses are therefore descriptive. With trajectories weighted equally, the compact score ranked near-slip windows above both prevalence and within-trajectory circular-phase controls under both definitions (representative average precision 0.310 versus prevalence 0.173; phase-null upper bound 0.257). Loading-history coordinates ranked more strongly, reaching 0.534 for causal elapsed strain. The recovery-aware rule retained 78.4% of activity-gated events and preferentially selected longer preceding intervals; ranking by time since the previous catalogued event remained compatible with a count-conditioned geometry null. Compact observables thus contain temporally aligned slip information, but stronger loading-history baselines and window-geometry sensitivity bound that evidence. These startup data do not isolate a state-specific short-horizon precursor beyond loading history or support a renewal interpretation of elapsed-strain ranking.

The electronic band structures of conventional band insulators generally remain unchanged under doping via chemical-potential shifts or increasing temperature. However, in Mott and Kondo insulators described by models such as the Hubbard and Kondo lattice models, distinct electronic modes with momentum-shifted magnetic dispersion relations have been shown to emerge from band edges into the gap. Here, by investigating the two-orbital Kanamori-Hubbard model, this study elucidates how and why the band structures of spin-1 antiferromagnetic insulators change with doping and temperature, revealing emergent spectral features characteristic of orbitally degenerate systems. The nature of the emergent electronic modes is clarified using weak-hopping effective theory, selection-rule analysis, and numerical calculations. In a typical parameter regime, the doping-induced modes in each orbital reflect distinct types of spin modes, while the temperature-induced modes primarily reflect the low-energy spin mode in both orbitals; in both cases, the emergent modes exhibit momentum-shifted spin-mode dispersion relations. The momentum regimes of these emergent modes can differ between orbitals if signs of the hopping parameters differ. For small inter-orbital repulsion, onsite spin-triplet pairs can form after doping, leading to a pair-breaking gap, while the temperature-induced electronic modes continue to reflect the low-energy spin mode without a pair-breaking gap. Moreover, the emergence and characteristics of electronic modes in nonequilibrium states by spin or charge perturbations are elucidated. These findings provide a comprehensive understanding of how the interplay among the spin, charge, and orbital degrees of freedom in large-spin antiferromagnetic insulators leads to emergent electronic modes, opening avenues for exploring unconventional quantum phenomena in strongly correlated systems.