Papers

Different field species can begin with finite anisotropic propagation geometries whose principal axes need not coincide. We ask whether local Yukawa interactions on a finite graph can nevertheless generate one common infrared spatial cone, even when the interactions that drive the locking become marginally irrelevant. Retaining the full finite mismatch between positive-definite spatial kinetic matrices, we derive the one-loop nonlinear matrix flow and show that its Thompson diameter is globally nonexpansive. On a connected graph, persistent normalized edge activity upgrades this to a uniform finite-window contraction, so all interacting sectors asymptotically share one relative propagation geometry. An explicit two-channel Pauli-Dirac Yukawa-quartic completion realizes the persistence conditions on an open weak-coupling set of finite-mismatch initial data. In four dimensions the Yukawa couplings vanish in the infrared, yet their accumulated interaction time diverges, leaving a Gaussian endpoint with a common spatial cone. For a controlled two-plateau extremal class, graph distance also fixes the first nonzero short-time order of the diameter decrease. Thus common-cone locking can emerge from renormalization-group dynamics rather than being imposed as a microscopic common structure.

We bound the error in ground-state expectations of local observables caused by truncating the spatial tails of a gapped quantum lattice Hamiltonian. We show that the error is controlled by the interaction strength discarded near each site, rather than by the extensive norm of the omitted Hamiltonian. If the gap remains open along a path that removes the interaction tail, the resulting bounds are uniform in system size and extend, under suitable assumptions, to thermodynamic-limit ground states. The convergence rate reflects the decay of the interaction tail: it is algebraic for power-law interactions, superpolynomial for superpolynomial interactions, and exponential at any strictly smaller rate for exponentially decaying interactions. For superpolynomial interactions, we also derive a direct infinite-volume estimate using automorphic equivalence. The results extend to isolated low-energy sectors and parity-even fermionic systems. For two-body interactions decaying as $r^{-p}$ in $d$ dimensions, we prove an error bound $O(R^{-(p-d)})$ for $p>2d$, where $R$ is the truncation range. We construct a gapped non-translation-invariant example that saturates this scaling, showing that the bound is optimal for the general class considered. Our results quantify when finite-range truncations faithfully reproduce the local physics of gapped long-range systems.

We propose several zero-point type arguments based on the inevitable zero point(s) of a spectral gap in the quantum spin system phase diagrams in various dimensions. We consider multi-parameter families of Hamiltonian extending the conventional zero-point theorem that includes only one parameter. Analogously to the zero-point theorem, we only impose model-independent transformation relations along the parameter boundary, rather than specifying any low-energy dynamics or response. We further give a series of conjectures, which generalize our statements in a uniform way. Our results give powerful and universal model-independent constraints on the possible relevant operators for critical phenomena in quantum spin models in arbitrary high dimensions.

A class of monitored topological invariants compares ordinary and symmetry-twisted quantum trajectories with identical stochastic records, so direct estimation requires exponentially costly matched-record postselection. We replace the twisted quantum experiment by uniformly randomized symmetry eigenstates with known charges, ordinary-boundary monitoring, and an offline twist decoder. Their correlation yields an exact finite-time response identity and removes this experimental sampling bottleneck. When the ordinary charge sharpens and the ordinary-to-flux deformation has trivial net readout-character flow, the response converges to the projective commutator of the symmetry-protected-topological phase; generator-pair responses then determine its finite-Abelian cohomology class. Spectator-sector crossings may close the global Lyapunov gap without changing this character-valued response. In monitored cluster circuits, the decoder is exact and polynomial in the Gaussian limit, while Gaussian-drop reconstruction treats interacting records; independent joint-sector spectroscopy and effect-state diagnostics validate the topological deformation.

Local measurements transform a many body wavefunction into a statistical ensemble of conditional quantum states. In chaotic systems, the higher moments of such ensembles diagnose the emergence of quantum state randomness, but their structure at equilibrium quantum criticality is largely unknown. Here we show that the projected ensemble of a Tomonaga-Luttinger liquid exhibits a universal nonlinear hierarchy of state overlap moments. Remarkably, the leading scaling exponents are independent of the continuously varying Luttinger parameter. Replica boundary conformal field theory reveals a geometric origin: outcome locking combines the active replica swaps into a single collective rotated sector, while intersecting compact replica branes eliminate the leading interaction dependent zero mode contribution. Matrix product state calculations across the interacting XXZ critical phase and direct free fermion calculations independently confirm the interaction independence and nonlinear hierarchy.

Entropy plays a central role in thermodynamics, statistical mechanics, information theory, and biology. However, its interpretation becomes increasingly ambiguous when information-theoretic concepts are applied to materials, including biological systems. For example, in biology, it is common practice to evaluate the entropy of DNA by enumerating possible configurations. This configuration entropy does not vanish at $T=0$, apparently contradicting the third law. Similar conceptual difficulties also arise in relating entropy to order, randomness, complexity, and information. In thermodynamics, entropy is a state function, and hence the entropy must be uniquely determined by a given state of a material. The crucial issue is therefore to identify the state variables that uniquely specify the thermodynamic state of a material. By establishing consistent definition of equilibrium and state variable, it is found that the time-averaged atom positions serve as the state variables of a solid. This leads to the important conclusion that a solid possesses many equilibrium states even at fixed temperature and volume. Entropy is not information but uncertainty associated with the state variables. The latter quantities convey the information of a material. This framework provides a unified thermodynamic basis of entropy, information, order, complexity, hysteresis, and residual entropy while preserving the third law. Frozen configurations and their activation resolve many longstanding ambiguities the thermodynamic evaluation of entropy.

We develop a unified fermionic-field formulation of the two-dimensional Ising model on several planar lattices using the Kac-Ward representation. Grassmann fields are associated with directed lattice links, while changes in the direction of fermionic trajectories are encoded by the corresponding Kac-Ward phase factors. The resulting quadratic action reduces, after Fourier transformation, to a finite-dimensional momentum-space fermionic matrix. Its determinant determines the excitation spectrum, while its zero modes define the critical surface. We apply this construction to the square, honeycomb, triangular, kagomé, and dual kagomé (dice or $T_3$) lattices. The known critical couplings of the homogeneous models are reproduced as consistency checks. For the fully anisotropic kagomé model with three independent couplings we recover the previously known fully anisotropic kagomé critical surface within the present Kac-Ward construction and the corresponding low-energy spectral equation. We construct the analogous $12\times12$ fermionic matrix for the anisotropic dice lattice and derive its critical surface, which is related to that of the kagomé lattice by the Ising duality transformation. The same fermionic formulation also provides direct access to physical correlation functions. Expressing the spin-spin correlators through fermionic Green functions and the corresponding Toeplitz/Pfaffian representation, we obtain the spontaneous magnetization of the anisotropic kagomé model and of the six-coordinated sublattice of the anisotropic dice model. In both cases the magnetization is controlled by the same spectral polynomial that determines the fermionic gap and vanishes on the corresponding critical surface. In the homogeneous limits the known results are recovered, and the standard two-dimensional Ising magnetization exponent $\beta=1/8$ follows.

The Maxwell-Demon nonequilibrium molecular dynamics method for measuring the shear viscosity divides the fluid simulation cell into two regions of width w in the $x$-direction, with the particles allowed to move freely between the two sides. The Demon maintains equal and opposite regional average particle velocities in the $y$-direction by applying an acceleration needed to sustain the nonequilibrium steady state (NESS), which includes both total force balance and an instantaneous correction for diffusion of particles across boundaries. We show that the driven velocity profile in x is a natural hydrodynamic response and not imposed by the constraint. For the present shear geometry, the measured NESS profile in Eulerian slabs is represented accurately by a piecewise parabolic form, reminiscent of planar Poiseuille flow. The parabolic profile gives an estimate of the kinematic viscosity from work done on the shearing fluid, as well as an entropy production estimate, derived from heat removal by the Nosé-Hoover thermostat that keeps each regional average temperature constant. We show that the mechanical work supplied by the Demon equals the heat removed by the thermostat. Once NESS driving is removed, the parabolic velocity profile relaxes exponentially in short order to sinusoidal, the natural transverse momentum-diffusion eigenmode. Our Maxwell-Demon shear method provides a direct NEMD formalism for obtaining shear viscosity from momentum diffusion, work, and entropy balances. Our results in three dimensions for increasing system size $N$ (the number of particles) demonstrate that shear viscosity approaches an asymptote (the so-called hydrodynamic limit) as $N^{-1/3}$.

Super-radiance is a striking phenomenon resulting from the collective interaction of emitters with light, and it is fundamentally related to the appearance of long-range correlations between the dipole moments of the emitters. As such, it represents a distinct phase of dissipative many-body systems compared to the case of independent emitters, similarly to how ferromagnetism stands out in magnetic materials in contrast to paramagnetism. In this work we address the conditions under which the transition to super-radiance can occur in ensembles of emitters subject to dephasing and individual decay – a situation which is particularly relevant to the case of emitters in the solid state. The simplifying assumption of an ensemble of permutationally invariant emitters allows for the efficient solution of both the dissipative dynamics after a pulsed excitation, as well as of the steady state under incoherent pumping. This exact solution allows us to benchmark a truncated cumulant expansion approach, which can give predictions for arbitrarily big system sizes. We show that super-radiance is fundamentally robust to sizable dephasing and non-radiative decay rates, both under a pulsed excitation, as well as under continuous pumping. This robustness is the result of the collective acceleration effect of super-radiant emission with respect to the individual coupling to a local environment. We establish the universal critical scaling laws at the transition between normal radiance and super-radiance; and we show that, in the super-radiant phase, significant finite-size crossovers can be observed before reaching the asymptotic scaling regime. Our results pave the way for future experiments to provide a quantitative characterization of the scaling properties of super-radiance, seen as a distinct non-equilibrium many-body phase in ensembles of incoherently pumped emitters.

Quantum resource theories characterize distinct forms of nonclassicality in many-body quantum states, raising the question of whether these resources evolve independently under generic ergodic dynamics. Considering diagnostics quadratic in the state, we show that the dynamics of different resource measures become mutually interdependent and are governed by a few common degrees of freedom. For Haar-random circuits, the purity together with a single resource witness suffices to reconstruct the remaining resource measures, as we demonstrate for coherence, various asymmetries, and number entropies. The same relations hold, to a good approximation, under chaotic Floquet and continuous-time Hamiltonian dynamics, establishing that this dynamical resource equivalence extends beyond random circuits. We further derive an exact coherence–imaginarity relation, remarkably accurate also beyond Haar-random circuits. Our results reveal an emergent simplification of many-body dynamics, in which sufficiently strong scrambling reduces seemingly distinct quantum resources to a few common dynamical degrees of freedom.

The crossover from long-range (LR) to short-range (SR) criticality in percolation has remained unsettled because previous renormalization-group (RG) analysis within the $\epsilon'=3\sigma-d$ expansion fixes the anomalous dimension at $\eta=2-\sigma$, whereas SR percolation has $\eta_{\rm SR}<0$ near $d=6$. Sak's matching condition then places the crossover above $\sigma=2$, outside the regime in which the LR interaction dominates. In spatial dimension $d=6-\epsilon$, we formulate a perturbative expansion for the LR $\phi^3$ field theory and perform a one-loop RG analysis throughout the perturbatively accessible nonclassical regime $0<\delta<\epsilon/3$, where $\delta = 2-\sigma$. We derive the one-loop corrections to the critical exponents $\eta$ and $\nu$, which acquire nontrivial dependence on $\epsilon$ and $\delta$. They reduce to their mean-field values at the LR upper critical line and continuously recover the SR $6-\epsilon$ results as $\sigma\to2$. These results support a crossover threshold $\sigma_*=2$ and remove the apparent discontinuity of $\eta$ between the LR and SR values within this framework. The same approach also yields the anomalous and edge exponents of the LR Lee–Yang universality class and $q$-state Potts universality classes with $q<2$.

We investigate a spin-$1/2$ anisotropic Heisenberg model on a lattice consisting of two identical bipartite sublattices. A family of exact eigenstates generated by the restricted spectrum generating algebra (RSGA) constitutes quantum many-body scar states, characterized by subextensive entanglement entropy and supporting. These scar states are magnon-pair condensates exhibiting off-diagonal long-range order (ODLRO). At the resonance point of the inter-sublattice interaction, the model exactly maps onto a mixed spin-$1$ and spin-$0$ XY model on a bipartite lattice, which decomposes into independent sub-Hamiltonians labeled by all possible spin configurations. Each spin-$0$ particle is dynamically isolated from its neighbors and acts as a kinetic constraint, giving rise to emergent Hilbert space fragmentation (HSF). Our work establishes an exactly solvable platform in which quantum many-body scars, magnon-pair condensation exhibiting off-diagonal long-range order, and Hilbert space fragmentation naturally coexist.

At cryogenic temperatures, phonons become one of the dominant energy carriers and thus can strongly influence the performance of electronic and sensing devices. In this work, we present a wave-mechanics based framework that predicts phonon transmission and thermal resistance of arbitrarily thick superlattices while retaining all acoustic branches, mode-conversion pathways, and angles of incidence. By enforcing phase coherence, our model predicts frequency-dependent transmission through arbitrary multi-layered structures.We use a genetic algorithm (NSGA-II) to efficiently select both materials and layer thicknesses. Our success criterion is that constituent layers satisfy the quarter-wavelength condition of the dominant phonon frequencies at a target temperature. This strategy identifies novel bilayer combinations that achieve thermal resistance of up to 3000 times greater than previously reported superlattices. The identified superlattices are poised to advance any technology that relies on coherent acoustic scattering, from ultra-low-temperature thermal insulation in superconducting flip-chip assemblies to phonon-blocking components in micro- and nano-electromechanical systems.

The standard Mott formula is widely used to describe thermoelectric transport, but it becomes less accurate when the temperature is not much smaller than the Fermi energy. In this work, we develop an all-orders extension of the Mott approach using a series of Riemann zeta functions. We show that when the transport function is a polynomial, the series ends after a finite number of terms, giving exact results within the model. We apply this method to graphene photothermoelectric devices using a quadratic conductivity model. The results provide closed-form expressions for the Seebeck coefficient, Lorenz ratio, and electronic figure of merit. The analysis shows that the Seebeck coefficient reaches a maximum instead of increasing indefinitely, while the Wiedemann-Franz law can be significantly violated at higher temperatures. We also find that disorder reduces the thermoelectric performance and that the electronic figure of merit has an upper limit in the clean graphene model. Finally, we discuss the effect of radiative heat transport on the figure of merit. These results provide a simple analytical way to study graphene thermoelectric transport beyond the usual low-temperature Mott approximation.

Free energies govern solid-state phase stability, yet computational materials discovery still relies largely on ground-state energies because free energy calculations require ensemble averages. We introduce the thermodynamic interatomic potential (TIP), which extends an interatomic potential from its static energy to a thermodynamically consistent Gibbs free energy model, with thermodynamic responses following from temperature and pressure by automatic differentiation. We implement TIP[UMA] using the universal potential UMA, train it on free energies from quasi-harmonic to molecular dynamics fidelity, and calibrate it to higher-resolution calculations or experiment. From a single evaluation, it returns the equation of state of a crystal and locates phase transitions among competing branches, including dynamically stabilized phases. Fine-tuning extends the model to alloy solubility limits and miscibility gaps. TIP makes the free energy as accessible as the potential energy, opening finite-temperature phase stability to high-throughput discovery.

Recent discoveries of two-dimensional (2D) ferromagnets have stimulated intense interest in understanding and controlling their spin transport properties. A central microscopic feature of these systems is that exchange-driven magnon–magnon interactions are strongly momentum dependent: low-momentum magnons interact weakly, while high-momentum ones can scatter strongly and exhibit collective hydrodynamic behavior. Understanding transport in such systems therefore requires a microscopic description capable of capturing ballistic and hydrodynamic regimes on equal footing. The natural framework is the quantum Boltzmann equation (QBE), whose solution is notoriously difficult because of the multidimensional collision integrals. Here, we develop a method based on an efficient representation of distribution functions as sums of Gaussians, which renders the collision integrals tractable. This approach enables accurate solution of the linearized QBE and computation of momentum- and frequency-resolved linear response in 2D ferromagnets across a broad range of temperatures and magnetic fields. In particular, we resolve a temperature-driven crossover from a ballistic regime dominated by weakly interacting low-momentum magnons to a collective hydrodynamic regime governed by strongly interacting high-momentum modes. Applying this method to monolayer CrCl$_3$, we obtain good agreement with recent nitrogen-vacancy-center dephasing experiments that reported anomalous magnetic noise consistent with magnon sound. More broadly, our work establishes a general framework for computing momentum- and frequency-resolved linear response in interacting 2D quantum systems describable within quantum Boltzmann kinetics.

A projective measurement of a many-body state produces a microscopic snapshot, usually viewed as random classical data. We show that partial occupation snapshots of the critical XX chain contain a universal angle with a precise conformal meaning. Dividing the ring into two measured and two unmeasured arcs, we assign geometry-dependent conformal side weights to the observed occupations and obtain a compact variable $\delta_L$. At every finite size, $\delta_L$ is fixed by the measured sites alone; the particular complete-configuration lift $X_L$ used in the proof additionally depends on unobserved particles. This angle is an exact microscopic compact coordinate whose scaling-limit law is that of the relative Dirichlet phase of the associated conformal quadrilateral—the boundary coordinate conjugate to charge in continuum post-measurement descriptions. Exact free-fermion determinants yield all of its Fourier moments. We prove that the lift becomes Gaussian with variance $2h(\zeta)$, where $h(\zeta)$ is the rectangle modulus, and hence $\langle e^{\ii q\delta_L}\rangle\to e^{-h(\zeta)q^2}$. Thus raw quantum snapshots realize the heat kernel on a circle and provide an outcome-level microscopic foundation for the compact zero-mode sector of Born averages over fluctuating conformal boundary conditions.

We study score-matching diffusion models with a convolutional architecture. We argue that the inductive bias of locality means that the machinery of effective field theory from physics can be usefully applied to describe the denoising dynamics. We apply this formalism first to a simple toy example which permits an analytical description, and thereafter to MNIST, and show that in both cases, the mutual information between two points grows in a manner predicted by a simple effective field theory of Brownian motion.

Entanglement spectra in gauge theories can encode both symmetry breaking and the organization of gauge sectors. In the two-flavor Schwinger model at vacuum angle $\theta=\pi$, we find that the joint Schmidt distribution $p_{Q_A,F_A}$, labeled by the subsystem gauge charge $Q_A$ and flavor imbalance $F_A$, reveals a cut-dependent gauge-sector hierarchy and a mass-induced flavor asymmetry: changing the staggered cut reorganizes the gauge-charge distribution $p_{Q_A}$, while mass imbalance breaks the $F_A\leftrightarrow-F_A$ symmetry of the conditional flavor distribution $p_{F_A|Q_A}$. Defining the combined weight $W_F^{(q)}=p_{q,+1}+p_{q,-1}$ and conditional polarization $\mathcal P_F^{(q)}=(p_{q,+1}-p_{q,-1})/W_F^{(q)}$, we find that changing the cut reverses the weight hierarchy, $W_F^{(-1)}>W_F^{(+1)}$ at unit-cell boundaries but $W_F^{(+1)}>W_F^{(-1)}$ at intra-cell cuts, while mass imbalance drives $\mathcal P_F^{(q)}$ away from zero with a $q$-dependent cut response. Symmetry resolution therefore separates gauge-sector ordering, sector weight, and flavor polarization that are mixed in the globally ordered entanglement spectrum.

Uncertainty relations provide lower bounds for otherwise hidden quantities of a partially accessible Markov network like the mean entropy production rate and the total dynamical activity. The thermodynamic uncertainty relation (TUR) is arguably the most prominent one and involves the precision of a fluctuating net current. One of its major generalizations is the multidimensional TUR (MTUR), which yields a tighter bound by using covariances of a set of observed net currents. We generalize this latter bound to time-dependently driven processes with arbitrary initial state and arbitrary measurement duration. Furthermore, this bound can be used with a set of fluctuating counting observables each of which can be time-antisymmetric, time-symmetric or time-asymmetric, i.e., a net current, a traffic or a flow. We can even allow for coarse-grained observations in which each counting observable could consist of multiple indiscernable observed transitions of the underlying system. Thus, we generalize the MTUR, extensions of the TUR for time-dependent processes based on one current, and an estimator based on one flux or on one traffic in a unifying way. We illustrate this general uncertainty relation with simple examples.

Perfect deterministic distinguishing of nonorthogonal quantum states is forbidden by the linear and unitary structure of quantum mechanics. It has often been assumed that, if such distinguishing were available, it would be the resource enabling work extraction from a single heat bath. We show that this expectation identifies the wrong thermodynamic operation and prove such hypothetical operation increases, rather than decreases, the joint entropy of system and detector. The entropy-decreasing resource is instead the inverse operation, which we call nonorthogonal-state erasure. Reanalyzing a Peres-type Szilard engine, we show that the apparent extracted work $W_{\mathrm{ext}}=0.2766k_{\mathrm{B}}T$ for an equal mixture of an atomic ensemble with spin state $\left|\uparrow\right\rangle $ and $\left|\rightarrow\right\rangle $. Thus the apparent second-law violation is supplied not by nonorthogonal-state distinguishing, but by a nonorthogonal quantum state erasure.

We show that the network of quantum register states of a quantum computer (QC), coupled through residual two-body interactions between qubits, exhibits small-world properties analogous to those of complex networks found in human society. The most probable Erdős number between any two states is about 9, comparable to the six degrees of separation reported by Milgram for social networks. Using the $\mathring{A}$berg criterion, which retains only interactions exceeding the local energy spacing, we construct an effective ($\mathring{A}$berg) network and show that, above a critical coupling strength, this network percolates into a giant component spanning nearly the whole quantum register space. This percolation transition closely matches the onset of quantum chaos and dynamical thermalization established previously via costly exact diagonalization, while our approach extends the accessible system size up to $n_q=30$ qubits.

We identify a broad class of nonthermal phases generated by the interplay of continuous symmetry breaking and weak nonequilibrium driving. Extending Kardar-Parisi-Zhang (KPZ) physics beyond the single $SO(2)$ chronon associated with periodically broken time translations, we construct nonequilibrium nonlinear sigma models for $SO(2)\times O(N)$ symmetry, describing non-Abelian time crystals with coexisting temporal and internal order. This symmetry structure arises naturally in driven quantum materials, active matter, and optically induced periodic states. For rotating and oscillating phases, we derive the Goldstone theories and show that chronon-$O(N)$ couplings remain finite deep in the ordered regime. One-loop renormalization group analysis reveals a KPZ-like dimensional structure: in $d=1,2$, arbitrarily weak nonequilibrium perturbations destabilize the equilibrium fixed point and generate strongly coupled nonthermal fixed points, realizing emergent equilibrium breaking. By contrast, for $d > 2$, weak perturbations are irrelevant and effective equilibrium is restored. A central result is unconventional weak dynamic scaling in the rotating phase: strongly coupled Goldstone sectors acquire distinct universal dynamical exponents despite belonging to the same order parameter. We characterize this scaling analytically and corroborate it through direct simulations in $1+1$ dimensions. In the oscillating phase, we recover and extend weak-scaling regimes known from drifting polymers. Finally, compactness and topological defects ultimately destroy long-range order but leave experimentally accessible nonthermal scaling windows. Together, these results extend KPZ universality to non-Abelian symmetry breaking.

Open system probes can provide an efficient means to characterize quantum many-body systems by employing them as engineered environments. The key idea is to map long-range spatial correlations of the environment onto dynamical correlations in the evolution of a simple quantum probe. Using the example of a qubit coupled to a transverse-field Ising model, we show how the non-Markovian rate or spectral flow can be used to identify stable and unstable fixed points, infer scaling dimensions of relevant fields, and deduce the renormalization group flow induced by deformations around any fixed point.

We uncover a mechanism for far-from-equilibrium topological phase transitions, via a one-dimensional compact phase model evolving deterministically from random initial conditions. It rests on topology and symmetry rather than on phenomenological postulates: phase compactness permits vortices, and a homogeneous fixed point suppresses their nucleation, with the fixed point itself implied by phase-shift symmetry. The competition between vortex-induced disordering and relaxation toward homogeneity drives a continuous nonequilibrium transition, whose universality class we identify as directed percolation (DP). We demonstrate this by constructing the corresponding effective field theory and numerically confirming DP critical scaling through dynamical-scaling analysis.

Liquids exhibit collective behavior that depends sensitively on thermodynamic conditions, interfaces and confinement, yet predicting each new state commonly requires a separate atomistic simulation. Classical density functional theory offers a reusable variational description, but its central excess free-energy functional is generally unknown, and learned approximations have largely remained restricted to planar or lower-dimensional settings. Here we show that this functional can be learned directly from fully three-dimensional equilibrium density fields while preserving spatial symmetry and variational consistency, without free-energy or chemical-potential labels. A single learned functional transfers across temperatures, system sizes and statistical ensembles, and recovers structure factors, the equation of state, liquid–vapor coexistence and interfacial broadening, none of which are used as training targets. Applied to complex three-dimensional geometries, it predicts the non-monotonic force associated with formation and rupture of a solvent-depleted bridge between colloids and adsorption in an interconnected gyroid pore. These results demonstrate that equilibrium density data can be converted into a transferable thermodynamic generator connecting microscopic liquid structure to response, phase behavior and collective phenomena.

We describe a mechanism of affine symmetry emergence in the maximal density regime of the prototypical model of self-organized criticality when the inverse square of the mesh of the underlying lattice is much larger than the number of random perturbation points distributed according to a prescribed probability measure supported in the interior of the ambient convex domain. Moreover, an appropriate scaling limit of the toppling function (aka odometer), which counts the number of operations per site, is a solution to a non-linear partial differential equation well known in the context of optimal transport and differential geometry, making it possible to accurately estimate the deviation of the density from its maximal value in any macroscopic window. The mechanism for the affine symmetry emergence is due to the novel empirical fact, supported in addition by inductive arguments that have recently being upgraded to a rigorous proof, that the scaling limit of the toppling function is the unique concave solution of the Monge-Ampère equation with Dirichlet boundary condition on the convex domain with the potential given by the probability measure used above as the infinite-perturbation profile.

Dyson universality typically manifests itself in local eigenvalue statistics. Here we show that its signature survives a nonlinear inverse-spectral reconstruction and reappears in the matrix geometry of the reconstructed operator. Using a dressing transformation, we map each unfolded spectrum to a deformation $f(x)$ of a fixed harmonic oscillator and represent it in the common oscillator basis by $F_{mn}=\bra m|f|n\ket$. We resolve the matrix-element weight into shells of fixed distance $d=|m-n|$, corresponding to the energy-transfer channels of the reference oscillator, and characterize the resulting distribution by distance-shell moments. Independently calibrated on Gaussian $\beta$-ensembles, these moments vary smoothly with $\beta$ and distinguish the GOE, GUE, and GSE. With this calibration fixed, applying the same diagnostic to the nontrivial zeros of the Riemann zeta function places the reconstructed operators in the GUE sector. Thus, the GUE character of the zeros is recovered not through direct statistics of the input levels, but from the distance-resolved geometry of the reconstructed operator.

We identify a general mechanism for the finite-time thermalization of macroscopic observables, such as coarse-grained charge densities, in terms of elementary forms of the quantum dynamics of initial states: (1) aperiodicity, which provides a computable measure of (2) a dynamical partially ergodic exploration of the Hilbert space. Specifically, this mechanism predicts the equilibration of all (concentrated) macroscopic observables, in almost all states in an initial ensemble and almost all times within finite and longer intervals, given only the observable-independent information that the return probability of the ensemble of initial states is small over a finite time range. As a special case, it also accesses standard results on equilibration over infinitely long times in terms of (stronger versions of) the effective dimension of initial state delocalization in the energy eigenbasis. Our results incorporate macroscopic thermalization into the domain of operational quantum statistical mechanics, recently developed to provide finitely computable criteria for microscopic thermalization. We discuss an overall characterization of this approach as establishing connections between (1) the decay of a (theoretically or experimentally) computable probe indicating memorylessness, (2) a fundamental invariant mechanism in terms of the alignment of observables or states in the Hilbert space, and (3) predicting different natural forms of (classical and) quantum thermalization, most of which rigorously recover conventional eigenstate-based descriptions of infinite-time thermalization as a special case but provide stronger accessible predictions over finite observation times in the thermodynamic limit.

Mesoscale self-assembly provides a route toward the design of programmable microsystems. Here, we construct flexible chains of floating monomers whose curved branches impose upward or downward deformations of the liquid interface, corresponding to effective positive or negative capillary charges. These geometrically encoded deformations generate local attractive or repulsive interactions along the chain. By tuning the capillary sequence, we obtain distinct folded configurations, including straight lines, zigzag patterns, and loops. For short chains, folding is largely governed by nearest-neighbor interactions and leads to well-defined structures. As the chain length increases and non-neighboring segments come into proximity and interact, however, the folding landscape becomes increasingly complex, with multiple metastable states whose number grows exponentially with chain length. We map these landscapes numerically and demonstrate experimentally that mechanical agitation allows the chains to transition between metastable configurations. Beyond encoding a target geometry, the capillary sequence therefore controls the complexity of the folding landscape as well as the degeneracy and mutational robustness of folded structures. These results establish capillary chains as a controllable mesoscale platform for investigating how local interaction rules give rise to collective folding and complex sequence-to-structure relationships reminiscent of those encountered in biomolecular systems.