Papers

Information sharing, threat perception, and collective evasion highlight the advantages of swarm intelligence. Here, we study the behavior of flocks of cognitive agents, based on numerical simulations of the augmented inertial spin model, with an explicit predator. Each agent on the predator-facing side of the flock perceives the threat, triggering collective turns through local interactions. We show that the augmented inertial spin model sustains nearly linear information propagation in the under-damped regime, even with realistic flocking interactions such as local collision avoidance and swarm cohesion in addition to alignment. The turning distance of the flock to a stationary predator scales with the ratio $\Delta_p/(v_0\sqrt{\eta})$, identifying an optimal balance between response strength $\Delta_p$, flock speed $v_0$, and damping $\eta$ of information propagation. Fragmentation arises when different parts of the flock turn in different directions, however, fast information propagation can synchronize these responses and maintain flock cohesion while under pursuit. For two predators, a combination of stability analysis and simulations reveals a stark contrast between flock and single-particle reactions, with scattering angle shaped by flock geometry, predator position, and the heterogeneous responses of the detecting front. Together, these results show how information propagation, flock geometry, and dynamics together shapes collective escape, providing general principles relevant to both biological flocks and robotic swarms.

We study magnets composed of molecules with atoms interacting via $SU(N)$-invariant two-body interactions. Atoms carry states transforming in generically different irreducible representations of $SU(N)$, and the interaction strength between atoms depends on the specific atoms involved. We derive the thermodynamics of these magnets in the mean-field approach, and find that they can exhibit mixed ferro-antiferromagnetic behavior. We present a full analysis of the simplest nontrivial case of molecules consisting of two atoms in the spin-$j$ representation of $SU(2)$, which generalizes conventional magnetic systems, and derive its phase structure and transitions.

Exponentially small spectral gaps are the central obstacle to adiabatic quantum annealing, yet whether such bottlenecks demand correspondingly complex entanglement remains unclear. We show that gap scaling and entanglement complexity need not be linked. Conventional first-order transitions combine exponentially small gaps with bounded $O(1)$ bipartite Schmidt rank, even though the critical states retain global multipartite correlations, while continuous transitions combine polynomially closing gaps with logarithmically growing entanglement. We show that each pairing can also be inverted: in a known first-order transition in a staggered-field antiferromagnetic Ising chain the gap closes polynomially despite bounded Schmidt rank, while we construct a mirror-twin manifold model whose gap closes exponentially even as its entanglement entropy grows logarithmically with system size. We derive bounds connecting Schmidt rank to Hamming-space geometry, and identify manifold density and connectivity as the ingredients that determine which combination occurs. These results show that entanglement complexity alone cannot characterize annealing difficulty, and point toward a broader search for quantum resources that capture the geometry of state evolution in Hilbert space.

We construct a family of chaotic brickwork quantum circuits exhibiting superdiffusive transport with dynamical exponent $z=3/2$ in the full Kardar–Parisi–Zhang (KPZ) universality class. This is enabled by the equilibrium current associated with a inhomogeneous conserved density having a nontrivial dependence on the chemical potential. Using nonlinear fluctuating hydrodynamics, we derive the propagation velocity, broadening scale, and universal scaling form of the charge correlation function from microscopic equilibrium properties. Tensor-network simulations of a two-site spin-$1$ (qutrit) circuit reproduce these parameter-free predictions, including the full stationary KPZ profile. We further construct a three-site spin-$\frac12$ (qubit) circuit, where transport varies from diffusive to superdiffusive with the chemical potential, while long-lived coherent quasiparticles delay the convergence of the profile to the KPZ scaling form. Our results establish that KPZ superdiffusion in quantum systems is not restricted to fine-tuned integrable models.

We study the emergent randomness in projected ensembles generated by dual-unitary circuits. Specifically, we consider evolution by solvable dual-unitary brickwork circuits followed by measurements on part of the system, which induce an ensemble of states on the unmeasured subsystem. Previous work has established that this projected ensemble of states forms a quantum state design in the limit where the bath size is large, but the rate of convergence at finite bath size has not been rigorously established. Under three inverse-polynomial assumptions, local permutation mixing, a bound on recurrent backward motion, and contraction at the measured boundary, we fill this gap and prove that a bath of polynomial size suffices to form approximate $k$-designs. In establishing our results, we develop a microscopic transport interpretation of emergent randomness in the projected ensemble, in which deviations from local permutation operators appear as defects, and make connections with the theory of quantum walks.

A spiking neuron is a dynamical system exhibiting a limit cycle (a spike) when subject to sufficiently excitatory input. Famous neuroscience experiments by Bryant and Segundo as well as Mainen and Sejnowski revealed that the spike times of some biological neurons are more reliable when subject to time-varying stimuli compared to constant ones. Provided with an industrial physics-based transient noise SPICE simulation framework compatible with foundry transistor compact models, we have demonstrated similar behaviours for a CMOS analog spiking neuron designed for neuromorphic computing hardware platforms. Under constant excitation current, the neuron operates in oscillatory regime and the empirical periods (interspike intervals) suffer from accumulated phase noise (jitter) during successive cycles, mainly due to the thermal noise of transistors. A time-varying input is reported to be capable of triggering output spikes according to a controlled statetransition mechanism, thereby significantly reducing the spike time jitter in the excitability regime. The physical limitation of the oscillatory or rate-coding regime in terms of reliabilitydissipation tradeoff is further evidenced by a stochastic thermodynamic uncertainty relation, a theorem that applies to general overdamped dissipative stochastic dynamical systems.

We develop an operational approach to strong-to-weak spontaneous symmetry breaking (sw-SSB) of a non-Abelian symmetry group G. We formulate it as the decoding task of distinguishing two strongly symmetric states that differ by a pair of inserted irreps, after both are corrupted by strongly symmetric decoherence. For finite G, this task is dual to distinguishing logical states of the quantum double D(G) under pure-charge noise. We derive a hierarchy of statistical mechanics models describing optimal decoding from the fusion outcomes measured on successively larger nested regions. As for maximum-likelihood decoders of Abelian codes the measured irreps act as quenched disorder obeying a Nishimori-like condition. Strikingly, because local irreps do not determine how they fuse globally, the strong $G\times G$ symmetry is realized only nonlocally, and irreps trivially charged under Z(G) (the center of G) can hide inside noise-generated ones. As a result, the strong symmetry spontaneously breaks down to Z(G), times the weak symmetry. The only transition at nonzero error rate is then an ordering of the center, whose threshold cannot decrease as the hierarchy is ascended. This conclusion holds at any finite level of the hierarchy for non-nilpotent groups. We confirm these predictions with tensor-network calculations for $S_3$ and SU(2). At the first level, the $S_3$ model, whose center is trivial, shows no transition, and the fidelity correlations of all irreps provably decay to non-zero values. The SU(2) model exhibits a $Z_2$ transition consistent with the Nishimori-Ising universality class, where the fidelity correlations of spin-$1/2$ irreps become long-range. The threshold rises from the first to the second level of the hierarchy by $16\%$. Our results provide a systematic framework for studying non-Abelian sw-SSB and for constructing decoders for non Abelian topological codes.

The Hohenberg-Mermin-Wagner theorem motivates the expectation that continuous symmetries remain unbroken in one-dimensional quantum ground states. Here, contrary to this expectation, we demonstrate the spontaneous breaking of U(1) spin-rotation symmetry and the emergence of an interacting quantum critical point in lattice spin-$1/2$ and spin-$1$ chains. Using subsystem Binder scaling, we locate the critical point and determine the correlation-length critical exponent as $\nu = 0.60 \pm 0.02$, distinct from the Gaussian value $0.5$ but consistent with the perturbative renormalization-group prediction. We further analyze the finite-size scaling of the lowest neutral excitation gap and obtain the dynamical critical exponent $z=1.986 \pm 0.005$. The result $z < 2$ is incompatible with microscopic realizations of this critical theory by frustration-free models, implying a mechanism for continuous symmetry breaking in one-dimensional quantum ground states distinct from frustration freeness.

We investigate the real-time dynamics of the Riesz gas (RG), a paradigmatic system of particles with power-law interactions that encapsulates several many-body interacting classical systems. While the equilibrium properties of the system have been extensively studied the connection between microscopic dynamics, macroscopic evolution and thermalization has remained largely unexplored. Combining extensive large-scale Newtonian simulations with a hydrodynamic framework formulated in terms of three coarse grained fields – density, velocity, and temperature – we establish a direct and quantitative correspondence between the two descriptions. The hydrodynamic theory incorporates two phenomenological transport coefficients, the bulk viscosity $\xi$ and thermal conductivity $\kappa$, which encode dissipative effects at a macroscopic level. By analyzing representative classes of initial conditions, such as dome-like and Newton-cradle-type profiles, we find excellent agreement between microscopic and hydrodynamic evolution over a broad range of timescales, starting from relatively early all the way up to times at which steady state is attained. Notably, this agreement persists across a substantial window of $\xi$ and $\kappa$, demonstrating the robustness of the emergent hydrodynamic description. Our results provide a systematic validation of hydrodynamics in the RG and establish a concrete bridge between Newtonian dynamics and continuum theories in systems with power-law interactions, starting from first principles.

What makes one quantum process more complex than another? We adopt an operational approach inspired by classical complexity science, which characterises structure through the memory required for causal generation. We develop a fully-quantum extension of computational mechanics for quantum space series: Correlated sequences of quantum outputs that do not return to interact with their generator. For stationary, memoryful quantum space series admitting finite-dimensional, primitive causal models, we show that any memory-minimal causal generator can be chosen to produce outputs isometrically, without a discarded environment. The resulting canonical matrix product state representation uniquely determines the irreducible memory required for generation. In particular, the minimum memory entropy is exactly the entanglement entropy across the past-future bipartition, giving entanglement a direct operational interpretation as irreducible memory for causal generation. The same structure determines the minimum memory dimension through the corresponding Schmidt rank. Within this class, we further show that the fundamental entropy rate vanishes, that causal generation is symmetric under time reversal, and that all memoryful processes possess infinite quantum Markov order with respect to arbitrary sharp measurements. These results establish an operational framework for quantifying intrinsic quantum structure, revealing deep connections between causal generation, complexity, memory, entropy, and entanglement.

Topological entanglements are central to understanding and predicting the properties of polymer melts. Yet, they make equilibrium sampling computationally challenging, as decorrelation times grow rapidly with chain length. Here, we introduce a Monte Carlo scheme that bypasses typical computational bottlenecks by working in a self-assembly ensemble rather than at fixed composition. Strictly local moves efficiently propagate backbone reconnections across scales while conserving the number of linear chains, achieving near-linear scaling of decorrelation time with system size, $\tau_{\rm eq}\sim V^{1.0}$. With this method, formulated for a fully-packed lattice, we equilibrate periodic systems totalling up to $\simeq 1.1\times 10^9$ monomers, accessing a universal melt regime insensitive to lattice details. We analyze intra- and inter-chain entanglements for chains of up to $N\simeq 5 \times 10^5$ monomers, revealing that they manifest as localized knots and links rather than as global tangles. Finally, we show that the magnitude of the Gauss linking integral between neighbouring chains grows only as $N^{1/4}$.

How do neural representations of neighbors become collective material behavior? Harmonic Theory (HT) reduces bearing representations to signed perceptual channels traceable to sensory acuity, decision dynamics, and interaction distance. Here we derive a nonlocal kinetic and hydrodynamic theory from the HT particle law without introducing heading alignment. The resulting fields retain HT's order-resolved perceptual spectrum and keep the neural and sensory origin of each coefficient visible. The theory predicts a torque-driven density instability: HT's direct-approach channel turns agents toward density excesses, while self-propulsion carries them inward. For isotropic spatial interactions and positive rotational diffusion, perceptual channel $n$ generically first affects conserved density at spatial order $k^{2n}$, and the full radial transforms select finite pattern wavelengths. Two populations can share the same long-wave instability threshold yet select different initial pattern spacings because their higher perceptual channels differ. Beyond onset, the one-particle continuum sustains a bidirectional nematic column; a prescribed, symmetry-allowed two-stream response amplifies a directional imbalance into sustained polar flow. In a distinct pure-repulsion regime, one-particle calculations show polar transport and translating transverse bands, with late pattern selection sensitive to numerical transport. The framework connects neural and sensory mechanisms to continuum coefficients, instabilities, and alignment-free collective motion.

We develop a finite-temperature field-theoretical description of the Casimir interaction between two perfectly conducting boundaries with the intervening gap filled by a two-component quantum Boltzmann plasma embedded in a homogeneous dielectric background. The quantum motion of the charged particles is represented by imaginary-time worldlines, while the electromagnetic field is treated in the Gaussian approximation. The resulting partition function contains distinct longitudinal and transverse response contributions and an additional quantum-induced source term with no classical counterpart. In the classical limit the theory reduces to the usual Casimir-screening picture: the static longitudinal mode is Debye screened, whereas the transverse electromagnetic sector is unaffected by classical mobile charges. Finite thermal de Broglie wavelengths modify the nonzero Matsubara response and produce the leading quantum correction to the force. In the static long-wavelength limit, the longitudinal dielectric function has, through the leading quantum correction, the same expansion structure as the Lindhard response of a degenerate electron gas under the correspondence $k_{TF}\leftrightarrow\kappa_D$ and $k_F\leftrightarrow\lambda_{dB}^{-1}$, while the static transverse response reproduces the leading high-temperature Landau orbital diamagnetic susceptibility.

We show that trap rotation overrides Kibble-Zurek (KZ) universality when a 2D Bose-Einstein condensate forms via a finite-time quench. In stochastic Gross-Pitaevskii simulations, the rotation-induced chiral bias drives the vortex number close to the Feynman-Onsager (FO) value, independent of the quench time. Ramping up rotation with the quench restores the KZ scaling at low frequencies, with vortex numbers below the FO value. The vortices form a disordered lattice that a pinning potential can order into an Abrikosov lattice, even at low rotation. Trap rotation thus offers a control knob for critical dynamics.

As electron sources are reduced in size, fabricated in new materials, or pushed for performance, the analytical formulations for thermo-field electron emission, namely Fowler-Nordheim and Murphy-Good equations and their JWKB-based extensions, are increasingly applied out of the range of conditions for which they were derived. We present GETELEC-3, an open-source code that replaces them with a direct numerical solution of the one-dimensional time-independent Schrödinger equation (1D-TISE). Several methods to solve the 1D-TISE have been implemented to test for speed, robustness, and solution's uncertainty. The Noumerov algorithm is found to be quickest, with the solution uncertainty below 1%, and together with an optimised kernel that advances all electron energies in parallel, the cost of calculating the current density is reduced to a few milliseconds - comparable to the JWKB evaluation. To further boost the calculation speed, especially in complicated barriers, a neural network has been trained on the residual of the logarithm of the semiclassical reference and it reproduces the current density better than 0.4% at a fraction of the computational cost. The code is developed for metals and semiconductors, accepts arbitrary potentials and density of states, and comes with a user-friendly interface and compiled executable to democratise rigorous electron emission calculations and data analysis.

We theoretically investigate the microscopic mechanism of melting in finite two-dimensional ion crystals confined in anisotropic traps. Building on our previous studies of melting probability as a function of temperature and anisotropy, we extend the analysis to crystal sizes ranging from $N=4$ to $N=101$ ions and examine how structural isomerization modifies the melting pathways. Using molecular dynamics simulations together with Metropolis-Hastings equilibrium sampling, we analyze radial fluctuations, angular disorder, Lindemann parameters, and isomer-dependent energy landscapes in these Coulomb crystals. We find that crystals with identical particle number and trap anisotropy can exhibit substantially different melting behavior depending on the metastable structural isomer they occupy. Contrary to a simple soft-mode instability picture, the observed melting process is characterized by a gradual thermally-driven accumulation of radial and angular disorder. Structural isomerization reshapes the fluctuation channels through which delocalization develops, leading to nonuniform melting probabilities across temperature and anisotropy space. These results provide a unified microscopic picture of melting in finite ion crystals and clarify the role of structural rearrangements in finite-size phase transitions.

The study of quantum memories out of thermal equilibrium is motivated both by the need for memories that withstand realistic noise in fault-tolerant quantum computers and by the fundamental question of when quantum memory can emerge in autonomous many-body systems. We establish a general equivalence between CSS-based quantum memories subject to Pauli noise and classical memories via two associated probabilistic processes. In the asynchronous setting, where the quantum dynamics is generated by a Lindbladian, we identify a broad class of syndrome-based Lindbladians for which the quantum memory problem is equivalent to memory in continuous-time classical Markov dynamics. In the synchronous setting, we introduce syndrome-based probabilistic cellular automata (SPCAs) and establish a one-to-one correspondence between their classical memories and CSS-based quantum memories under local quantum channels. This framework provides a systematic route for deriving and constructing quantum memories from classical probabilistic processes, and recovers known results, including the fact that the 4D toric code is a quantum memory in the presence of thermal noise. As an application, we give the first rigorous proof that the 4D toric code with Toom's rule is a quantum memory in the presence of local Pauli noise, provided the error is below a constant threshold. We prove this both for the corresponding synchronous, PCA-type quantum dynamics and for a Floquet Lindbladian. More generally, we show that classical memory in an SPCA can be lifted to a quantum memory under Floquet Lindbladian dynamics; whether this can be done with a time-independent Lindbladian remains open. Our results provide a general framework for relating classical and quantum memory, shed light on the conditions for fully autonomous quantum memories, and may guide the construction of provable autonomous quantum memories in low dimensions.

Sompolinsky and Zippelius obtained Parisi's solution of the Sherrington-Kirkpatrick (SK) model from the relaxational dynamics of soft spins in continuous time, by assuming a hierarchy of widely separated time scales. Here we carry out the same programme for a discrete-time dynamics in which all Ising spins are updated at once. This dynamics, synchronous Monte Carlo (SyncMC), introduces Gaussian auxiliary fields so that the spins become conditionally independent, and it samples the Boltzmann distribution exactly for any system with symmetric pairwise couplings. We show that, for any such system, the correlation and response functions of SyncMC obey an exact fluctuation-dissipation relation in discrete time in equilibrium. The dynamical mean-field equations of SyncMC for the SK model contain two terms absent in continuous-time dynamics, a self-coupling of each spin and a noise correlated through the couplings; both affect only the fast relaxation. As a result, under the same assumptions as in the Sompolinsky-Zippelius construction (widely separated time scales, and on each slow scale the same relation with a reduced ratio x, as expected in relaxation from random initial conditions), the long-time structure of SyncMC reproduces the Parisi equations, including the Parisi partial differential equation and the equation for the distribution of local fields. Equilibrium simulations with replica exchange for up to N=2048 spins exclude the replica-symmetric distribution of the actual local fields and are consistent with the Parisi solution. The function x(q) estimated from the overlap distribution, and from the response in relaxation from random configurations for up to N=4096 spins, is also consistent with Parisi's.

We generalize the Furusawa–Kaneko model, a simple model of intracellular catalytic reaction networks, to multicatalyst reactions and analyze the generalized model using dynamical mean-field theory. In the thermodynamic and dense-network limit, we derive exact effective equations and analyze their fixed points for arbitrary degree distributions. Under nutrient-poor conditions, network heterogeneity suppresses the metabolic–starvation transition irrespective of the number of catalysts per reaction. In contrast, under nutrient-rich conditions, the bifurcation structure changes with the number of catalysts. With one catalyst per reaction, only continuous transitions occur, whereas two or more catalysts give rise to bistable phases and discontinuous transitions. The bifurcation structure also differs between two and three catalysts per reaction, with three catalysts allowing bistability between metabolic states with different cell growth rates. Our results provide a possible mechanism for bistability and abrupt switching in metabolic dynamics.

In a finite zero-field Ising chain, the all-up configuration and zero magnetization become equally likely at a single coupling. This crossing has recently been described as a thermal transition of the finite chain, an analogue of a first-order transition temperature, and approximated by an analytic estimate and a numerical fit. We find its asymptotics, with explicit constants, for free and for periodic ends. The coupling at the crossing grows like half the logarithm of the length of the chain, minus half the logarithm of that logarithm. So the correlation length at the crossing is a vanishing fraction of the chain. Periodic ends lower the coupling at the crossing by an amount that decays like the inverse logarithm of the length. The earlier approximations lack the doubly logarithmic term, which explains why a fit on chains of moderate length finds a slope below one half. The proofs treat the magnetization as the position of a persistent random walk and compare its central probability with a modified Bessel function, with a relative error bound that is explicit for every length. For free ends this traps the crossing in an explicit interval at every length. The proof is analytic for long chains and uses exact integer arithmetic for short ones. We also locate, for each smaller magnetization, the coupling at which it becomes as likely as full magnetization.

We investigate a class of dynamic percolation models on a lattice, in which connections are added and removed by a set of local stochastic rules. In particular, the removal of any connection that can result in one connected cluster becoming two (or more) separate clusters is strictly forbidden. These models include and are inspired by a model for local quantum error correction for a toric code studied by Chirame, et al., PRX Quantum 6, 030363 (2025), who identified a phase transition with first-order characteristics, such as bistability and a discontinuous order parameter. We show numerically that this transition is a hybrid percolation transition (HPT), having characteristics of a continuous percolation transition such as diverging critical clusters while at the same transition having discontinuities like a first-order transition. We then modify this model to be fully isotropic, showing that the HPT remains. In both of these models, the steady state on one side of the HPT is an absorbing state; by turning on additional isotropic local stochastic moves, we remove the absorbing state and strongly suppress or remove the first-order transition, leaving an apparently continuous percolation transition. Curiously, the numerically-observed percolation critical exponents do not change significantly between the models with hybrid transitions and the model with an apparently continuous transition. These exponents are significantly different from known percolation transitions, indicating that this may be a new universality class.

Many physical inverse problems are mediated by expensive stochastic simulators for which response gradients, adjoint sensitivities, or a differentiable simulator interface are unavailable. We introduce Multiple Target-based Confident Acquisition (MUTACO), an uncertainty-aware sequential-design method for response matching that requires only noisy forward evaluations and learns the multicomponent response together with its predictive uncertainty. We develop and evaluate MUTACO for a disordered network of stochastic phase oscillators. The inverse task is to infer statistical properties of the local potential and interactions from macroscopic rotation and synchronization curves under multiple driving conditions. Rather than requiring unique recovery of these statistical properties, MUTACO searches for parameter configurations whose predicted rotation and synchronization responses are compatible with the target response while accounting for predictive uncertainty. This response-centered formulation is appropriate when experimentally accessible observables characterize ensemble statistics rather than a particular microscopic realization. Under strictly limited simulation budgets, MUTACO achieves the lowest held-out response error among the tested adaptive-search, space-filling, and simulation-based inference methods, while also yielding lower parameter-recovery error than the compared methods. These results demonstrate that response-targeted sequential design is a simulator-efficient approach to inverse modeling from finite noisy forward evaluations and suggest broader applicability to stochastic physical systems with correlated multicomponent responses and weakly constrained parameter directions.

Nonreciprocal interactions have emerged as a fundamental driver of collective behavior far from equilibrium. Here, we show that nonreciprocal couplings between spin systems whose isolated dynamics favors ordered states, beyond the previously identified oscillatory (swap) phase, give rise to a richer nonequilibrium phenomenology, including a multistable regime where ordered and disordered states coexist, a scenario strictly forbidden in equilibrium. Crucially, we show that this nonequilibrium phenomenology is inherited directly from the critical properties of the underlying isolated model. In particular, tricriticality in the isolated system gives rise to multistability, hysteresis, and hard excitations in the oscillatory dynamics, while non-normal interactions further enrich the phase diagram by generating multistability. Moving beyond mean-field theory, we derive a universal field equation governing the onset of these nonreciprocal oscillations in finite dimensions. Our results establish a unified theoretical framework connecting critical phenomena, dynamical systems, and non-reciprocal collective dynamics, with applications ranging from opinion dynamics to active matter

Self-propelled particles that only repel one another can still separate into a dense and a dilute phase, a process known as motility-induced phase separation (MIPS). In a clean system the domains coarsen like any conserved mixture: domains grow as $\ell(t)\sim t^{1/3}$. Living and synthetic swimmers, however, move through rough, porous, or patterned surroundings. Using large-scale simulations of active Brownian particles, we ask how frozen heterogeneity changes MIPS coarsening. We introduce disorder in two ways, as a quenched random force field acting on particle positions and as a quenched random torque field acting on their orientations. Both destroy Lifshitz-Slyozov growth. A transient power law with a disorder-dependent exponent gives way to activated dynamics in which the effective dynamic exponent grows without bound and domains grow at most logarithmically. The crossover obeys the scaling form known from the random-field Ising model, and the domain morphology depends on disorder strength, so superuniversality fails. The two kinds of disorder act through different mechanisms. Random forces trap particles in the sinks of a random drift field once the drift beats self-propulsion. Random torques act as a sign-random, quenched chirality that erodes persistence and lowers the local Péclet number toward its critical value. Our results show that quenched disorder is a relevant perturbation for the kinetics of active phase separation and connect MIPS coarsening to the physics of pinned interfaces in disordered magnets.

Dielectric screening of electric fields is modified by interfaces and confinement, and any accurate description of interfacial chemistry necessitates properly modeling the nonuniform dielectric tensor. However, models with short range interactions, such as local machine learned interatomic potentials (MLIPs), are increasingly used in simulations of molecular interfaces without quantitative understanding of their nonuniform dielectric response. To build this understanding, we use the framework provided by local molecular field (LMF) theory to quantify the roles of short and long range electrostatics in confined water. Short and long range models predict the same transverse dielectric profile but short range models predict qualitatively different longitudinal dielectric profiles than their long range counterparts. To understand these differences, we develop a Landau theory that shows that long range interactions stiffen polarization fluctuations by a factor of the bulk dielectric constant and reduce the interfacial polarization correlation length by an order of magnitude. LMF theory, which captures long range interactions with an averaged field, can correct the structure and dielectric response, but the standard fluctuation relation no longer holds. We derive a fluctuation relation and integral equation for LMF theory and demonstrate their accuracy for predicting longitudinal dielectric response. MLIPs that incorporate interfacial configurations in their training essentially learn a static mean field correction at the interface, such that the integral equation can be used to predict their nonuniform dielectric profile from polarization fluctuations. We also show that short range MLIPs can be combined with symmetry preserving mean field (SPMF) theory to provide a linear-scaling alternative for long range interactions and predicting nonuniform dielectric functions.

The decay of out-of-time-ordered correlators (OTOCs) to a small residual value signals the scrambling of quantum information. This behavior is generic: it occurs in both chaotic and interacting integrable many-body systems, and therefore cannot by itself distinguish between them. In this paper we analytically study the late-time saturation value of a closely related observable, operator purity, and show that its scaling with system size robustly distinguishes chaotic from integrable systems. Our approach is based on the Mazur bound, which provides concrete scaling estimates and makes explicit why the locality of integrable charges matters. We support our findings with numerical simulations of one-dimensional spin chains.

A mutant gene that appears in a finite population will, in the long run, either disappear from it or become fixed, so that all members of the population will carry a copy of the mutant gene. Determining the fixation probability of a mutant gene is thus a prerequisite for modeling evolutionary dynamics in finite populations. Within the diffusion theory framework, the mutant's competition with the wild-type genes is described by the closed-form solution of a one-dimensional backward Kolmogorov equation for the mutant fixation probability, derived by Motoo Kimura in 1962. However, in asexual populations the rate of adaptation and the relative importance of alternative evolutionary pathways are shaped by clonal interference - the competition between several lineages arising from distinct beneficial or deleterious mutations. Quantitative descriptions of clonal interference require computing fixation probabilities in populations where multiple alleles are present simultaneously - a formidable mathematical problem which amounts to solving a multi-dimensional backward Kolmogorov equation. Here, we employ fluctuation theorems (a set of exact equalities in non-equilibrium statistical mechanics) in order to re-derive Kimura's fixation probability formula. When extended to multi-allele systems, fluctuation theorems provide a constraint which must be satisfied by any valid set of fixation probabilities. Moreover, we present a recursive analytical solution of the multi-allele fixation probability problem. We use our formalism to study the fate of a novel beneficial mutation in a clonal interference scenario, discovering substantial deviations between our exact treatment and the mean-field approximation in which the target mutation competes with a single effective genotype. Our formalism can be used to replace both explicit simulations and approximate analytical results in models of asexual evolution.

The article contains exact results for the behavior of the Casimir force of Ising chain of $N$ atoms containing an impurity atom. The force is considered as a function of $N$ and on both the temperature $T$ and the external magnetic field $h$. The interactions between nearest neighbors within the chain are supposed to be of a ferromagnetic short-ranged type $J>0$. The impurity atom interacts with constants $J_{ia}$ with its nearest neighbors, where $J_{ia}$ can be both of ferromagnetic type, i.e., $J_{ia}>0$, as well as of antiferromagnetic type, i.e., $J_{ia}<0$. It turns out that the Casimir force can be both attractive or repulsive, depending on the sign and the magnitude of the ratio $J_{ia}/J$.

We examine the dc driven transport of particles with Yukawa interactions through an assembly of chiral active particles undergoing circular motion. The driven particles exhibit a jammed phase, a nonlinear disordered or plastic regime where there is a finite Hall effect produced by interactions with the active chiral particles, and a high drive linear regime where the driven and nondriven particles phase separate and the Hall effect nearly disappears. The chiral particles experience strong drag and Hall effects from the driven particles, and these effects vary monotonically with changing thermal fluctuations or chiral motion parameters. The different dynamical phases are correlated with features in the longitudinal and transverse transport curves, and we map out the phases as a function of active orbit size, thermal fluctuations, and particle density.

Ising machines have emerged as promising hardware accelerators for intractable optimization and sampling problems, yet their practical impact increasingly hinges on the co-design of algorithms and hardware, where algorithmic demands shape new architectures and new hardware capabilities inspire entirely new algorithms. In this Review, we survey probabilistic algorithms designed for portability across diverse Ising platforms, advocating a top-down perspective that prioritizes principled methods with provable guarantees. We cover foundational methods such as simulated annealing and parallel tempering, including two-dimensional extensions that natively encode hard constraints, and examine approaches that expand the scale of solvable problems from cluster mean-field methods to variational samplers. We highlight the Probabilistic Approximate Optimization Algorithm (PAOA), a classical analog of QAOA that emerged directly from probabilistic hardware development, and explore how generative AI and Ising machines might reinforce each other: learned models propose global moves to accelerate optimization, while probabilistic techniques improve inference in large language models. Much as quantum computing has seen algorithms co-evolve with hardware, probabilistic and Ising computing stand at a similar inflection point. We outline a co-design framework for accelerating the capabilities and adoption of next-generation Ising machines.