Papers

Retarded thermal correlators, analytically continued to complex frequency, exhibit non-hydrodynamic poles and branch cuts that constrain hydrodynamics. We construct Gaussian Schwinger-Keldysh effective actions in which branch cuts arise from continua of relaxation poles and response functions are governed by Stieltjes transforms of relaxation-time densities. Dynamical KMS symmetry, positivity and stability constrain the spectra, while endpoint behaviour controls the local branch structure and near-edge pole scaling. The illustrative examples of uniform and power-law densities exhibit respectively beyond-all-orders pole-endpoint separation and a continuous interpolation between pole-pole and pole-branch-point termination. Finally, we show that an energy-dependent relaxation-time approximation in kinetic theory provides a microscopic realization of our branch cuts at zero momentum.

Completeness is widely recognized in quantum information as an important property of a family of monotones, because it ensures that no information relevant to state conversion is lost. We show that completeness is also physically important in many-body systems: an incomplete measure of symmetry breaking can miss essential features of symmetry-restoration dynamics. We study the logarithmic characteristic function (LCF), also known as the string order parameter, whose full family is complete for exact i.i.d. pure-state conversion under symmetry-preserving operations for finite groups. We introduce a fidelity-based extension of the LCF to mixed states and identify two concrete advantages over entanglement asymmetry (EA). First, for a finite symmetry group $G$, EA is bounded by $\log |G|$ and can approach the same saturated value for different initial states in the thermodynamic limit, making their relaxation curves indistinguishable and preventing the identification of a discrete-symmetry Mpemba effect. By contrast, the LCF can remain extensive, with a coefficient that depends on the initial state and time, and therefore continues to distinguish their relaxation dynamics. Second, different LCF components can exhibit distinct relaxation and crossing behavior, including cases in which EA shows no crossing. We demonstrate these advantages in spin-chain quenches and a single-qubit system under depolarizing noise. We also develop a replica construction for the fidelity-based LCF in quantum field theory and derive analytical results for conformal field theory.

We investigate the utility of the locality-preserving Derby-Klassen (DK) fermion-to-qubit mapping [arXiv:2003.06939] for variational quantum simulation of two-dimensional $t$-$V$ and Fermi-Hubbard models. The DK mapping preserves the locality of fermionic interactions with an enlarged Hilbert space, thereby requiring additional constraints that define the physical sector. We incorporate these constraints directly into a Hamiltonian Variational Ansätz (HVA) through Clifford-gate state preparation and use the Variational Quantum Eigensolver (VQE) to show that the low-energy properties of the resulting qubit Hamiltonian are accurately reproduced. We further exploit particle-number conservation inherent in the ansätz to resolve distinct symmetry sectors and reliably access degenerate states. Consequently, we benchmark the DK-HVA against Jordan-Wigner-based variational circuits at nonzero chemical potential, where particle-hole symmetry and the associated half-filled sign-free condition are absent. Finally, we demonstrate the advantage of locality-preserving mappings in higher-dimensional fermionic systems, where the conventional Jordan-Wigner (JW) transformation generates increasingly long Pauli strings and corresponding circuit overheads. We further extend the framework to the spinful Fermi-Hubbard model and identify a tradeoff between fermionic-mode placement and the locality of hopping and on-site interaction terms. These results establish a practical framework combining locality-preserving fermion-to-qubit mappings, constraint-preserving Clifford state preparation, and symmetry-preserving variational circuits, that trades auxiliary-qubit and stabilizer-preparation overhead for reduced operator nonlocality, providing a practical route toward resource-efficient quantum simulation of higher-dimensional interacting fermionic systems.

We show that an $O(1)$ local defect is sufficient to generate approximate unitary $k$-designs from an otherwise integrable quantum many-body system. Using a two-Pauli-kick (2PK) protocol with temporal sampling, we demonstrate this mechanism in a fixed-magnetization sector of deterministic XXZ spin chains with a single integrability-breaking bulk defect. We derive an analytical selection rule for the Pauli kicks and show that symmetry-preserving strings with a specific domain-wall count, fixed by the couplings, govern design formation. An exhaustive search over all admissible Pauli strings identifies a broad family of kicks that produce designs in the chaotic regime, whereas no such kicks exist in the integrable limit, including for boundary defects. We further show that the design-forming mechanism remains effective for weak bulk defects as the system size increases.

Recent experiments demonstrating superconducting-like characteristics in materials above their equilibrium transition temperatures following strong sub-picosecond optical excitation have stimulated theoretical interest in phase-disordered superconductors subject to a periodically modulated superfluid stiffness. Previous analyses of the single-layer optical conductivity have shown that such a drive can enhance the low-frequency $1/\omega$ response, even when the period-averaged stiffness remains unchanged. We extend these studies to bilayer systems, such as the YBa$_2$Cu$_3$O$_{6+x}$ (YBCO) cuprate, by considering drives with different symmetries. Specifically, we investigate a layer-symmetric drive, in which the two planes stiffen and soften simultaneously, and a layer-antisymmetric drive, in which one plane stiffens while the other softens. Both drives enhance correlations of the layer-averaged phase and generate comparable superconducting-like optical conductivities. Only the symmetric drive, however, strengthens relative-phase locking and the associated counterflow response to a magnetic field parallel to the planes. Thus, an enhanced $1/\omega$ optical conductivity does not by itself imply enhanced magnetic screening. In view of applications to driven YBCO, where superconducting-like in-plane optics and transient diamagnetism have both been reported, our result provides a symmetry diagnostic: within a phase-synchronization mechanism, the experimentally active low-frequency stiffness modulation must contain a substantial layer-symmetric component.

The nitrogen-vacancy (NV) center in diamond is a prominent quantum-sensing platform. Combining readout at the quantum projection noise limit with strong dipolar interactions promises substantial gains in sensitivity. However, experimentally accessing this regime has remained a longstanding challenge. In this work, we demonstrate quantum-projection-noise-resolved readout of a strongly-interacting, two-dimensional ensemble of NV centers. Our approach leverages repetitive readout via the NV's intrinsic $^{15}$N nuclear memory at a moderate magnetic field ($\sim 0.3$ T), improving the readout fidelities by nearly an order of magnitude. This enables us to directly resolve the quantum projection noise of a coherent spin state and to watch the ensemble's intrinsic dipolar interactions shear this noise into an anisotropic profile. Our results open the door to direct measurements of spin squeezing and entanglement-enhanced sensing in the solid state.

Spiral spin liquids are magnetic states whose classical ground-state manifold consists of planar incommensurate spin spirals with wave vectors lying on a continuous ring or surface in reciprocal space. The resulting subextensive degeneracy suppresses magnetic long-range order and gives rise to liquid-like behavior. Despite numerous material realizations and theoretical investigations, the structure of low-temperature spin configurations of spin-isotropic Heisenberg spiral spin liquids has remained poorly understood. Here, we classify and characterize the classical topological defects supported by these systems. We uncover a rich family of vortex types involving concerted windings of spin directions, spiral-plane normals, and wave-vector orientations, yielding a $\mathbb{Z} \times \mathbb{Z}_2$ classification. Remarkably, the elementary defects are half-vortices carrying fractional $2\pi$ windings in both spin and momentum space and obey fusion rules resembling to those of Ising anyons. Large-scale classical simulations of a square-lattice spiral spin liquid reveal that these vortices are dense in the spiral-spin-liquid regime, and bind tightly below an order-by-disorder phase transition, eventually fusing to vacuum.

The last decade has seen the development of powerful methods for learning complex structure from high-dimensional data. These advances have brought to the foreground fundamental connections between subdisciplines of physics, applied mathematics, and machine learning. In this review, we bring together some of these ideas, often expressed in different languages, to highlight a conceptual thread that links five distinct fields: control theory, optimal transport, probabilistic inference, non-equilibrium thermodynamics, and machine learning. A common theme is the optimization of free-energy-like functionals under dynamical or statistical constraints. We offer a guided tour through this thread and present selected applications in reinforcement learning, variational inference, and generative modeling. The review does not assume prior familiarity with these topics, and begins with principles originating from physics.

We study finite-state approximations to a chiral nematic lattice model whose local directors are embedded in three-dimensional orientational space. The model analyzed here is formulated in terms of a rotated quadrupolar interaction, which provides a direct angular chirality parameter $\Delta$ and reduces to the usual planar chiral-nematic form for directors confined to the xy plane. On a rooted Cayley tree, the statistical problem is written as a nonlinear recursion for branch partition functions. In the infinite-coordination limit, with $rJ_Q$ fixed, the recursion becomes a softmax map for the state probabilities. We analyze Cartesian three-state, planar four-state, and non-planar four-state discretizations. The first supports ordered and period-two attractors, whereas the planar four-state discretization displays a sequence of commensurate and longer-period modulated attractors. Its disordered fixed point loses stability at $t=9/16$ through a complex-conjugate pair with phase $q=\pm 2\Delta$, so a modulated critical mode is selected for every nonzero chirality. The non-planar four-state set is intrinsically anisotropic and, when the stated model is reconstructed directly, supports prominent period-three as well as period-two and higher-period cycles. Because attractor stability does not by itself establish global thermodynamic stability, the diagrams reported here are interpreted as attractor/stability diagrams rather than equilibrium phase diagrams.

Likelihood-based network models are often fitted under links' independence and low-order constraints, while empirical networks frequently exhibit systematic higher-order structures such as triangles and wedges, characterizing the observed clustering patterns. Real-world core-periphery networks such as the interbank market or the air transportation system represent key examples, with cores displaying complex and nonlinear features. We formalize Penalized Likelihood with Structural Discrepancies (PLSD) as an inference-level correction that trades likelihood fit for agreement with targeted motifs. PLSD augments the negative log-likelihood with a penalty on standardized wedge and triangle discrepancies, yielding a controlled distortion of the likelihood surface that can be interpreted through a linear response analysis. A calibration approach for the unique tuning hyperparameter is introduced to turn off the penalization term when the model is correctly specified, thereby recovering maximum-likelihood estimation in that case. We then introduce a mixed-constraint maximum-entropy core-periphery Exponential Random Graph Model (ERGM), derive unconditional semi-closed motif formulas under Pareto-distributed core fitness, and interpret sparse-regime scaling through a big-jump mechanism for heavy-tailed distributions. We finally corroborate the PLSD inference methodology both with Monte Carlo simulations of a toy stochastic block model and by applying the novel core-periphery ERGM to weekly eMID interbank networks (2009-2015) and monthly US air traffic networks (1991-2000). We show that PLSD describes cores that are not only dense but also higher-order-rich and captures the observed heterogeneous degree distributions and the overexpression of wedges and triangles, at a link-level cost proportional to the model misspecification.

We characterize the magic of random fermionic Gaussian states through their Pauli spectrum and their stabilizer entropies. For the Haar ensemble of Majorana Gaussian states we derive closed finite-$N$ expressions for the average stabilizer purities and reconstruct the Pauli spectrum exactly, as a mixture of products of beta-distributed variables resolved by Majorana weight. The stabilizer entropies, and their filtered versions, freeze at Rényi index $q_c=2$: for $q>2$ the magic density is $1/(q-1)$, controlled by rare weight-two Majorana strings. Resolving these contributions requires exponentially many characteristic samples, making direct sampling estimates of the stabilizer entropies inefficient in this frozen regime. For Haar-random Gaussian states at fixed filling, we express the averaged stabilizer purities at positive integer $q$ as coefficient integrals over $\mathrm{SU}(2q)$, with dimension independent of $N$, and evaluate the $q=2$ case exactly. We establish that the frozen density describes typical states in the Majorana and half-filled number-conserving ensembles and relate these ensembles to the corresponding $\mathrm{SYK}_2$ ground states. Finally, we show that typical fermionic Gaussian states retain certified magic after discarding any fixed fraction $\kappa<\kappa_\star^{\rm G}\simeq0.7613$ of their modes in the thermodynamic limit, remaining magical even beyond the $2/3$ threshold for Haar-random states in the full Hilbert space.

The framework of superstatistics can be used to describe non-Maxwellian single-particle velocity distributions as mixtures of Maxwellian distributions, where the weight is imposed by a probability density associated to the inverse temperature $\beta = 1/(k_B T)$. Among the typical model choices for $\beta$ are gamma, inverse gamma and lognormal distributions, sometimes called the universality classes of superstatistics. Given a set of observed velocities, however, there is no direct method to determine the underlying temperature distribution, as temperature itself is not a phase-space observable, and numerically inverting the Laplace transform is an unreliable process. In this work, we show that Jaynes' principle of maximum entropy can be used to successfully reconstruct the inverse temperature distribution from data, by using the logarithmic moments of the kinetic energy as constraints. Although the kinetic energy distributions for the three universality classes are almost indistinguishable at the same mean and variance of $\beta$, the method correctly discriminates between them.

The efficiency of a machine at the scale of thermal fluctuations is random, and the conventional ratio $-W/Q_h$ has no moment of any order: its input heat fluctuates through zero. We work instead with the exergetic ratio $\eta=W/(W+T_0S)$, which lies in $[0,1]$ pointwise for non-negative dissipation, and ask what the energy budget alone determines about its mean. With $\alpha=T_0\langle S\rangle/W$ and $\sigma^2$ the relative variance of the dissipation, $1/(1+\alpha)<\langle\eta\rangle\le\sigma^2/(1+\sigma^2)+1/\{(1+\sigma^2)[1+\alpha(1+\sigma^2)]\}$, both ends sharp, with no distributional assumption. The floor is Jensen's inequality: fluctuating dissipation raises the mean efficiency above its deterministic value, and the mean alone gives nothing more. The ceiling is attained by an intermittently reversible law, dissipating nothing in a fraction $\sigma^2/(1+\sigma^2)$ of realisations, a prediction testable on trajectories. A third moment lifts the floor. Fixed delivered work is not required: when it too fluctuates, the bounds hold with the moments taken on $T_0S/W$, and the thermodynamic uncertainty relation on the work current converts the ceiling into a precision-efficiency frontier, whose zero-variance member is the known bound on a motor's ratio-of-means efficiency, shown here to be unsafe for the mean of the fluctuating ratio. Inside the interval lies the maximum-entropy benchmark $\alpha^{-1}e^{1/\alpha}E_1(1/\alpha)$. Finally the bounds are worked out for a motor with futile cycles, observed until a fixed number of steps is delivered. There the dissipation cannot fall below the reversible cost of that work, and this floor $b$ sharpens the ceiling to $q/(1+\alpha b)+(1-q)/(1+\alpha c)$, $q=\sigma^2/[\sigma^2+(1-b)^2]$, $c=1+\sigma^2/(1-b)$, removing 40-67 per cent of the width. It is saturated when slips are rare: the extremal law is an operating regime, not an idealisation.

We establish a complete information-theoretic framework for the known minimum-energy configurations of the two-dimensional Thomson problem on a hard-wall disk, based on the Shannon entropy of the Voronoi topological charge distribution. Two exact results are proven and hold for all studied systems of size $N=12$-$10^5$. First, an entropy balance law decomposes the total entropy into bulk, boundary, and mixing contributions without approximation. Second, a topological charge sum rule fixes the total charge at twice the number of boundary particles plus six; together with the observed separation of bulk and boundary coordination numbers, it yields exact relations between the populations of three- and four-coordinated boundary particles and the bulk charge. We further prove that the boundary entropy is bounded by the binary maximum and that saturation of this bound is equivalent to the bulk charge per boundary particle approaching minus one half, a regime that the framework itself restricts to boundaries of at least twelve particles. All identities are verified numerically to machine precision, locating bulk nucleation at $56$ particles, the maximum of global disorder at $146$, and the onset of boundary saturation beyond about $1000$. The framework carries over to closed spherical geometry, where the total charge is fixed at twelve.

We study an ordered polar active flock on a torus and show that topological sound persists on a compact curved surface without topological defects or physical boundaries. Using the covariant Toner Tu theory, we derive an effective nonHermitian Dirac operator whose curvature-induced mass changes sign across the outer and inner equators, producing two Jackiw Rebbi domain walls. These support co-propagating but distinct chiral edge excitations: a density mode localized on the positively curved outer equator and a Goldstone mode localized on the negatively curved inner equator. The bulk bands possess opposite half-integer Chern numbers whose jumps across the domain walls are determined by the sign of the Gaussian curvature. We further show that the localised modes are protected by a one-dimensional Callias index theorem, while the sum of the local indices obeys the Poincare Hopf theorem on the compact surface. Our results establish that curvature alone, independent of defects and boundaries, is sufficient to generate and protect topological sound in active matter, providing a unified connection between non-Hermitian topology, differential geometry, and hydrodynamic theory of collective motion.

Active matter is liable to invent protocols that evade the constraints of equilibrium thermodynamics. We put forward active pistons that extract work by periodic compression alone without changing any bulk property of the system. Such pistons necessarily couple the perturbation imposed by an external operator with some degrees of freedom internal to active components. We illustrate this design principle with elastic networks composed of self-aligning motile particles. For slow protocols, self-alignment always overwhelms mechanical friction when the internal activity exceeds a specific threshold controlled by fluctuations. We identify the key response coefficient that helps delineate regimes of work extraction, and reveal that the corresponding phase diagram follows a master curve with re-entrance in terms of noise amplitude. Overall, our active pistons embody a novel design principle with broad implications for building innovative engines far from equilibrium.

Near many-body localization crossovers, local memory fluctuates strongly among eigenstates and ensemble realizations, but the observed heterogeneity combines contributions from different statistical levels. We develop a statistical framework based on configuration-space distance distributions that uses a variance decomposition to separate fluctuations within eigenstates, between eigenstates of one sample, and between samples. Applying this framework to random-cosine and quasiperiodic-cosine Ising ensembles with the same one-site field marginal, we find that, at the exact-diagonalization sizes studied, the clearest difference occurs among disorder realizations or quasiperiodic phase samples, whereas within-eigenstate and within-sample eigenstate-to- eigenstate contributions remain broadly comparable. Spatial covariances show that random outer fluctuations have a much stronger uniform component, whereas quasiperiodic phase fluctuations are organized more strongly at finite wave number and partly cancel in the spatial average controlling the distance center. We find that, near the crossover in the random ensemble, the ensemble-averaged distance center is particularly sensitive to changes in the nominal field strength. Combined with sample-to-sample differences in the realized field amplitude, this mean response accounts for much of the sample-to-sample variation in the distance center. Analysis of half-chain entanglement further shows that its sample-to-sample fluctuations likewise reflect the combined effects of amplitude variations and its own mean response. An application to a fixed-magnetization spin chain demonstrates the framework in a constrained configuration space. Resolving both statistical level and spatial mode therefore provides a more complete picture of sample- dependent many-body memory and its configuration-space probability geometry.

Dense suspensions can undergo a dramatic increase in viscosity at a critical value of the shear stress. This phenomenon, termed discontinuous shear thickening (DST), has been attributed to an increase in the fraction of particle interactions becoming frictional with increasing shear stress, and a successful mean-field theory has been developed to explain various accompanying rheological properties. On a microscopic scale, however, conventional structural analysis measures such as the grain-position pair correlation function show no significant changes with the onset of DST, though recent work has shown that similar analysis in the dual space of contact forces does lead to marked changes at this transition. Furthermore, experimental results have suggested the existence of higher-order microscopic correlations and the importance of incorporating fluctuations away from a mean-field description. To this end, we use a higher-order cluster analysis tool to study the force networks obtained from simulations of dense suspensions to construct an effective interaction potential in force space. We show that there are significant changes occurring in this potential as a function of density and stress close to DST. We discuss the implications of these observations on an emergent field theory of the DST transition.

Black holes are conjectured to be maximally chaotic, with their quantum spectra expected to exhibit universal random-matrix correlations. This expectation, however, has so far rested largely on holographic descriptions or on many-body models in which randomness is introduced rather than derived from the microscopic degrees of freedom of the horizon itself. In the horizon matrix model, the fuzzy sphere supports highly degenerate parton states whose multiplicity accounts for the black-hole entropy. We show that quantum fluctuations of the horizon geometry lift this degeneracy and generate an ensemble of one-parton Hamiltonians. Both the operator structure and the rank-dependent covariance of this ensemble are determined by the microscopic model, rather than fixed by quenched couplings. Despite this structured covariance, the resulting spectra exhibit GOE, GUE, and GSE statistics dictated by their antiunitary symmetry classes, with the adjacent-gap statistic becoming increasingly self-averaging with matrix size. The model also realizes the universal Pandey–Mehta orthogonal-to-unitary crossover, with the crossover scale determined by the microscopic geometric covariance. A rank-resolved variance analysis shows that the fluctuation strength remains broadly distributed across tensor ranks up to the microscopic cutoff, providing a microscopic basis for the observed Wigner–Dyson universality and effectively nonlocal dynamics. The antiunitary symmetry acts directly on the fuzzy-sphere geometry, so the Dyson class of a conditional Hamiltonian is determined by the antiunitary symmetry of the underlying quantum geometry. This provides a microscopic counterpart of the Stanford–Witten relation between geometry and random-matrix universality in JT gravity. These results establish a microscopic route from quantum horizon geometry to black-hole spectral chaos.

The characteristic feature of counterflow superfluids consisting of $N\geq 3$ components – the so-called Borromean supercounterfluids (BSCF) – is the presence of $N$ distinct elementary topological excitations (vortices) despite having only $N-1$ independent Goldstone modes. We show that this remarkable property clearly manifests itself at the Berezinskii-Kosterlitz-Thouless-type transition from the BSCF to the normal state, under the conditions of slight to moderate deviations from the case of exact intercomponent symmetry. More generally, our analysis also applies to any multicomponent superfluid with intercomponent drag fine-tuned to the value when certain composite vortices compete energetically with elementary ones.

Unlike in Anderson localization - where any amount of uncorrelated disorder localizes all eigenstates in one dimension - a one-dimensional system with quasiperiodic potential supports a richer range of localization behavior. This paper investigates the fundamental question of which potential characteristics govern localization properties. We characterize quasiperiodic potentials using two independent parameters, correlation and bias, and demonstrate that bias, in addition to correlation, critically influences localization. Through the study of an extended Aubry-André model, in which a tunable parameter allows systematic control over both the bias and correlation of the potential, we show that bias is key in determining the fraction of delocalized states. An increase in the potential strength generally enhances the tendency toward localization, while simultaneously strengthening the correlations in the quasiperiodic potential. This apparent counterintuitive behavior can be understood in terms of the bias parameter: increasing the potential strength reduces the bias, which in turn favors localization. For the family of Hamiltonians considered, we identify two critical bias thresholds: below the lower threshold, the entire spectrum is localized, whereas below the higher threshold, at most a fraction of the states can be delocalized, precluding delocalization of the entire spectrum. To further test our framework, we examine a quasiperiodic model with zero bias and find that, despite its correlated nature, all states become localized even at very weak potential strengths - recovering the Anderson-like scenario.

We derive an extension of the generalized Kibble-Zurek mechanism (KZM), which provides a stochastic approach to defect formation, to reverse quench protocols. While the universal scaling behavior of defects in reverse quenches has been observed previously in certain 1D chains, we argument from a probability-theoretical perspective that this scaling persists in general, and is given by the double of the defect density variance in forward quenches. We validate these results analytically for the one-dimensional transverse field Ising model and numerically for its bond-disordered variant governed by an infinite randomness fixed point. Starting from the paramagnetic phase, this protocol relies solely on global control of the system's magnetic field and global magnetization measurements, enabling the extraction of critical exponents without microscopic access to individual defects. This approach offers a robust and experimentally feasible method for probing quantum critical behavior through entirely global operations.

We investigate the equilibrium thermodynamics and thermodynamic Riemannian geometry of an ideal quon gas within the grand canonical ensemble. By incorporating the algebraic deformation parameter $q$, the system generalizes standard bosonic behavior while recovering the conventional ideal Bose gas in the undeformed limit. A rigorous examination of the ground-state occupation reveals two disconnected mathematical domains of the fugacity. By enforcing thermodynamic continuity, single-valuedness, and consistency with the high-temperature classical limit, we exclude the second mathematical branch and establish the lower interval as the unique physically admissible state space. This identifies the deformation parameter as an intrinsic, generalized Bose–Einstein condensation threshold. Employing the Fisher-Rao metric on the equilibrium parameter manifold, we probe the thermodynamic scalar curvature across all temperature regimes. The scalar curvature remains strictly positive throughout the physical domain, confirming that the deformation preserves an effectively attractive statistical interaction without inducing fermionic tendencies. Near the critical condensation threshold, the curvature increases sharply and exhibits a definitive divergence, providing an unambiguous geometric signature of macroscopic coherence and critical fluctuations. Below the transition temperature, the pinning of fugacity eliminates a fluctuating degree of freedom, collapsing the scalar curvature to zero.

What is the least dissipative finite Markov machine that can reproduce a given stochastic process exactly? A basic compactness worry is that a minimizing sequence might lower its cost only by sending microscopic rates to infinity, never converging to an actual finite-rate machine. We prove that this escape is impossible at fixed hidden dimension. States of vanishing stationary occupation can be traced out, and infinitely fast conductance classes can be contracted, without increasing entropy production or losing the limiting observed path law. Hence the exact-law cost $V_n(P)$ is attained and lower semicontinuous at every fixed state count, with no cap on rates or mean activity. Adding a positive price $\kappa$ per used hidden state yields an attained optimum over all finite dimensions and an exact representation by globally calibrated lower certificates built from finitely many observable path expectations. The lower envelope $G_\kappa(P)=\min_n[V_n(P)+\kappa n]$ defines an architecture phase diagram whose slope is the selected state count; divergence of that count as $\kappa\downarrow0$ is equivalent to failure of any finite machine to attain the all-dimension infimum $V_\infty(P)$. For the two-block renewal family $P_q$, we derive complete finite-dimensional phase-type cancellation equations, give an explicit four-phase counterexample to a tempting restricted parameterization, and prove strictly positive minimal dissipation at every feasible finite dimension for all $0<q<1$. These results reduce the remaining problem to one sharp question: can growing hidden architecture drive the dissipation of $P_q$ to its all-dimension infimum without any finite optimizer, and in the strongest scenario, to zero?

We investigate and compare a range of indicators for glassiness in monodisperse magnetic and non-magnetic soft-sphere fluids at low temperatures with a view to exploring the effect of the magnetic moment. We perform extensive molecular dynamics simulations using the Stockmayer model for magnetic fluids and a pure Lennard-Jones interaction for the non-magnetic case. Our investigations involve quenching experiments, in which both systems are rapidly cooled deep below their freezing temperatures. Although the Lennard-Jones fluid forms compact aggregates, the inclusion of dipolar interactions promotes the development of branched and open morphologies. After characterizing the static properties of the frozen structures, we focus on their dynamics. A key observable is the self-part of the van Hove function, which measures the probability that a particle is displaced by a distance $\Delta$ over time $t$. In both fluids, this function exhibits non-Gaussian behavior — thereby providing a signature of dynamic heterogeneity and glassiness. This behavior stems from a separation of time scales between two distinct processes: mobile particles that escape their environments and immobile particles that vibrate within cages. In particular, we find a heavier tail in the van Hove function for the Stockmayer fluid, which is a consequence of the strongly correlated motion in chain-like structures found there. These findings shed light on core relaxation mechanisms in magnetic fluids, advancing our understanding of magnetically responsive colloidal systems.

We derive exact analytical expressions for higher-order correlations of Gaussian level-set interfaces, establishing a direct link between bulk field statistics and interface geometry. This framework enables efficient reconstruction of disordered media, detailed modeling of {Gaussian foams}—structured, double-thresholded interfaces with tunable morphology—and analysis of {memory-enhanced anisotropy} reflecting directional persistence in surface structure. These results open new possibilities for characterizing complex transport, guiding stochastic reconstructions, designing materials with desired properties, quantifying the information content of correlation functions and modelling directional processes on irregular boundaries.

We investigate local conserved quantities in non-Hermitian bosonic lattice systems whose underlying Yang–Baxter structure remains unclear. Focusing on a one-dimensional bosonic chain with quartic interactions of creation operators, we provide a new representation of the local conserved quantities previously constructed by Sanatani and Shiraishi. Using Fourier transformation and trigonometric identities, we systematically derive these conserved quantities and show directly that they form a mutually commuting family. We further extend the construction to interactions extending beyond a single site, cubic interactions, asymmetric hopping, and an on-site potential. Our results provide a unified framework for constructing and characterizing local conserved quantities in this class of non-Hermitian many-body systems.

Oscillator Ising machines (OIMs) provide an analog dynamical approach to combinatorial optimization, but comparatively little is known about the statistical structure of the ensembles they generate. Using the Sherrington-Kirkpatrick (SK) spin-glass model, we introduce a selective oscillator scheme, OIM+, in which successive annealing epochs are combined with energy-based elimination and repopulation of replicas. We characterize the resulting states through overlap distributions, Hamming distances, hierarchical clustering, and local-field statistics. OIM+ explores structured low-energy regions while retaining a nontrivial ensemble of configurations despite repeated selection. We identify sparse weak-local-field residual defects as a characteristic limitation of the dynamics. A short Metropolis-Hastings refinement preferentially corrects these defects, indicating that the oscillator dynamics performs the dominant collective exploration while the remaining corrections are predominantly local. The weak fields arise mainly from cancellation among competing interaction terms rather than uniformly weak couplings. The same behavior persists for an antiferromagnetically biased SK ensemble, where the hybrid method reaches a pooled mean energy comparable to a substantially longer pure Metropolis anneal. The complete protocol also achieves competitive performance on standard G-set Max-Cut benchmarks. These results suggest a natural division of labor between collective analog search and targeted local refinement.

We determine statistics of allele-frequency trajectories across replicate populations. Defining $R = 2N_e|s|$ where $N_e$ is the effective population size and $s$ is the additive selection coefficient of a focal allele, we focus on strong selection which corresponds to $R \gg 1$. Strong selection does not require large selection coefficients: in populations of realistic size, it can readily arise from small selection coefficients. Our analysis concerns a biallelic locus over timescales on which mutation can be neglected. Every allele-frequency trajectory belongs to one of two absorbing classes: fixation or loss. When $R$ is large, individual allele-frequency trajectories can appear nearly deterministic. This does not imply that an approximation of allele-frequency statistics can be based on a single deterministic trajectory. For a beneficial allele, the deterministic trajectory approaches fixation, yet a non-negligible fraction of stochastic trajectories may be lost. Ignoring trajectories that achieve loss can produce severely erroneous statistics. We address this by conditioning separately on the eventual loss and eventual fixation of the focal allele. This yields an outcome-conditioned representation of a statistic. In the strong-selection regime, we apply a small-noise expansion that reasonably captures transient behaviours of statistics while recovering their exact long-time limits. We illustrate results with numerical examples for the mean allele frequency and its variance. The biological interpretation of this work is that, even under strong selection, both trajectory types are of importance. We provide a simple framework for calculating time-dependent allele-frequency statistics relevant to experimental evolution, longitudinal population-genomic data, and the dynamics of alleles driving selective sweeps.

We study a one dimensional lattice model of coupled driven system where two kinds of hardcore particle species, `light' and `heavy', move on a fluctuating landscape. Light particles prefer to move upward along the local height gradient of the landscape, and heavy particles prefer to move downhill. In addition, these particle species also exert bias on the local height profile. The unoccupied or vacant parts of the landscape experience no bias and undergo symmetric height fluctuations. In an earlier work, we had derived a phase diagram of the system consisting of different kinds of ordered and disordered phases. In the ordered phase, one or both particle species phase-separate, while the landscape forms a large hill or deep valley. Here we study coarsening by monitoring the development of long-range order in the particles and landscape from an initially disordered state. Unlike conventional phase-ordering systems, where coarsening proceeds through the formation and merger of ordered domains, here we find that domains formed at early times become unsustainable at later times. Instead of merging together, these early domains disintegrate and new domains emerge which finally give rise to large scale ordered structure in the long time limit, resulting a highly unusual coarsening behavior. For particle coarsening, the characteristic length scale grows with two distinctly different power law exponents at early and late times. The landscape coarsening is even more dramatic where the length scale decreases for brief time-intervals, instead of increasing continuously. The height fluctuations of the landscape shows periodic oscillations with time during the coarsening phase. Using linear hydrodynamics we explain that this is caused by three normal modes which move through the system like travelling waves. We calculate the propagation velocities of these modes within mean field approximation.