Papers

We formulate a non-Abelian theory of network compatibility in which dynamical transformations reside on the links. Gauge covariance follows from the freedom to choose local representation frames, while plaquette holonomies quantify the incompatibility of closed-loop transformations. For an SU(2) model on the complete simplicial 2-complex with quenched random plaquette couplings, parallel-tempering simulations reveal a continuous disorder-driven phase transition characterized by the network compatibility $M_P$. As the disorder strength approaches the critical value, the compatibility drops rapidly to a value that decreases with system size, while the frustration energy of the network sharply rises. Moreover, analysis of connected replica-overlap width provides no evidence for thermodynamic replica-symmetry breaking. Instead, the high-disorder regime sustains a nearly constant integrated adjacent correlation as the system size increases. Therefore, rather than a frozen gauge glass or a featureless disordered “gas” phase, dense topological frustration produces a non-glassy correlated gauge liquid in which individual pair correlations are geometrically diluted while a finite integrated correlation survives.

In the transcriptional networks of Escherichia coli and Saccharomyces cerevisiae, the eight feed-forward loop (FFL) motifs occur at markedly different frequencies. Although previous studies have linked the abundant C1- and I1-FFLs to specific dynamical functions, a common account of the broader pattern is lacking. To address this gap, we adopt an information-theoretic approach. An FFL transmits information through two paths that share an input and converge on an output, suggesting that their interaction may contribute to differences among motifs. To investigate this, we decompose input-output mutual information (MI) into pathway MI and interference MI (IMI). Here, the pathway MI collects the contributions of individual pathways, whereas IMI identifies the contribution that arises from their interference. We find that within a representative parameter regime, IMI values of FFLs produce a hierarchy that closely resembles the abundance ordering in E. coli, whereas total and pathway MIs do not. Motivated by this observation, we perform constrained optimization that identifies parameter regimes compatible with abundance-like targets for both S. cerevisiae and E. coli. We relate the optimized IMI hierarchy to pathway interference strength and local pathway sensitivities to understand the underlying biophysical origin. Our framework thus probes the correspondence between pathway interference, information transmission, and motif-abundance hierarchies.

Singular kicked rotors have long been compared with power-law random banded matrices (PRBM) because their momentum-space Floquet matrix elements decay algebraically. However, it has remained unclear whether the deterministic correlations of the rotor become irrelevant at long distances and, consequently, under what conditions the two systems share the same infrared theory. To address this question, we derive a nonlocal supersymmetric nonlinear sigma model directly from a quantum kicked rotor with a power-law or logarithmic singularity. By carrying out the renormalization-group analysis up to two-loop order, we show that, after matching the symmetry class and coupling convention, the rotor reproduces the long-range Anderson transition of the corresponding PRBM, including its localized, critical, and extended infrared regimes.

Quantum magnets provide a microscopic platform for studying confinement and gauge-constrained structures mediated by emergent gauge fields. We investigate confined spinon complexes in the columnar valence-bond-solid (VBS) phase near deconfined quantum criticality using pinned-spin defects and quantum Monte Carlo simulations. The pinned spins act as static spinon sources with controlled positions, spin projections, and VBS vorticities, enabling measurement of defect energies and direct real-space visualization of the associated VBS domain-wall strings. For matched spinon-antispinon sources, the excitation energy saturates beyond a characteristic separation as one extended dipole reorganizes into two shorter neutral dipoles, providing energetic and real-space evidence of string breaking. We further show that domain-wall connectivity is governed by lattice-scale VBS phase offsets in addition to vorticity and spin-projection neutrality. Compatible multi-pin patterns generate connected four-spinon complexes and extended domain-wall networks that retain their global connectivity under local distortions. These results establish pinned-spin defects as a controlled tool for assembling and resolving multi-spinon structures and their confining strings in a VBS phase.

Bose-Einstein condensates of photons in dye filled microcavities are known to feature many properties of the ideal bose gas at thermal equilibrium. Nevertheless, the finite photon life time renders them driven dissipative systems where losses are balanced by continuous driving by a pump laser. We show here with simulations based on a classical field model that their driven-dissipative nature causes their first order coherence to feature Kardar-Parisi-Zhang (KPZ) scaling, a phenomenon well known in the related condensates of exciton-polaritons. Remarkably, we find that the KPZ scaling even occurs in a regime with large density fluctuations. We discuss the modification of the scaling by the occupation of excited states and how to recover the universal scaling behavior by spectral filtering.

Nonequilibrium statistical mechanics is the science of time as it manifests itself in the transient or steady entropy producing dynamical condition of many-body systems. Beyond the vivid multiformity of the phenomena themselves, three foundational issues lie at its heart. The first question concerns the very origin of entropy production, which gives macroscopic processes their direction and thereby defines the arrow of time: how does an atomistic mechanical world give rise to dissipated heat, thermalization, and time-reversal symmetry breaking? The second asks why, far beyond the familiar behavior of equilibrium systems, driving or agitation may produce and select stable and functionally rich structures: what is it about far-from-equilibrium, low-entropy driving that unleashes the wealth and intricacy of the natural world? The third issue is partly methodological: to determine how, and for which subclass of such wildly diverse nonequilibrium systems, a systematic, unified description and modeling from first principles remains possible. This essay addresses these issues in an informal, semi-popular-science style, offering a personally engaging yet wide-ranging introduction to the complementary roles of entropy production and the less familiar, more recently coined notion of frenesy in the dynamical fluctuations of steadily driven systems. Together, we argue, they provide a more complete starting point for understanding physical time on mesoscopic to macroscopic scales.

We prove the absence of nontrivial local conserved quantities in a class of $U(1)$-symmetric spin-$1$ chains with nearest-neighbor interactions in which some of the quadrupolar couplings vanish, a class that is not covered by previous studies. Applying the technique of Shiraishi to these systems, we show that, for every model in this class on a periodic chain of $N$ sites, there is no $k$-local conserved quantity for any $3\le k\le N/2$. In particular, for a frustration-free spin-$1$ chain that exhibits spontaneous $U(1)$ symmetry breaking at zero temperature in one spatial dimension, we prove that every local conserved quantity with support up to half of the system size is a linear combination of the identity, the total magnetization $S^z$, and the Hamiltonian itself. This rigorously establishes that, unlike the Heisenberg ferromagnet, the model admits no local order parameter commuting with the Hamiltonian, so that its continuous symmetry breaking is enabled by the frustration-free structure rather than by a conserved order parameter. We also prove the absence of $k$-local conserved quantities for $3\le k\le N/2$ in the periodic Motzkin chain, a frustration-free spin-$1$ chain closely related to the original Motzkin chain, for which spontaneous $U(1)$ symmetry breaking at zero temperature has also been reported.

The interplay between non-Hermiticity and localization has attracted considerable interest, yet the driven dynamics of localization transitions in non-Hermitian systems with on-site gain and loss remains largely unexplored. Here we investigate the critical scaling behavior and driven dynamics of the non-Hermitian Aubry-André (AA) model with on-site gain and loss. Through finite-size scaling analyses of the localization length, the inverse participation ratio (IPR), and the energy gap, we extract the critical exponents $\nu = 1.00(2)$, $s = 0.7965(2)$, and $z = 1.999(2)$. These exponents are different from those of both the Hermitian AA model and the nonreciprocal hopping AA model, particularly the IPR exponent $s$, demonstrating that the gain-loss mechanism belongs to a distinct universality class. For the driven dynamics, we focus on the case where the system is initially prepared in a gapless extended state and linearly driven across the critical point. We verify that the finite-time scaling (FTS) framework remains applicable provided that the criterion $z' < r$ is satisfied, where $z' = 1.999(2)$ characterizes the gap closure in the extended phase and $r = z + 1/\nu \approx 2.999$. The predicted FTS scaling forms for the IPR are numerically validated across a wide range of system sizes and driving rates, demonstrating that the unified scaling description can be successfully generalized to the gain-loss type non-Hermitian AA model. Our work not only establishes the gain-loss AA model as a new universality class of localization transitions but also extends the applicability of the FTS framework to non-Hermitian systems with gapless initial states.

The simulation of rare macroscopic events in stochastic network dynamics, such as widespread epidemic outbreaks, cascading failures in communication networks, or the escape from metastable states in many-body systems, is severely hindered by methodological challenges like catastrophic rejection rates, weight degeneracy, genealogical correlations, and critical slowing down inherent to standard forward-time algorithms, splitting methods, and transition-path sampling. Conditional-path Monte Carlo (CPMC) overcomes these limitations by employing non-local Swendsen-Wang-like cluster updates that operate directly on full-system trajectories. Serving as the technical companion to [Sun, Moody, and Barthel, arXiv:2608.16171], this paper provides the rigorous mathematical foundations and algorithmic details underlying the CPMC framework. We formally define the joint path-graph probability weights and derive the transition and uniformization sum rules that guarantee detailed balance. Applying the framework to susceptible-infectious-susceptible (SIS) models, we systematically construct and optimize single-node and edge graph vertex sets specifically designed to prevent lock avalanches and maintain the structural mobility of the epidemic trunk. Furthermore, we detail a dynamic programming scheme to exactly implement complex boundary conditions - including patient-zero and macroscopic outbreak-size constraints - enabling the rejection-free generation of valid trajectories. Finally, we assess the computational complexity of the algorithm, describe parallelization strategies, and validate CPMC against exact solutions for dynamics on small networks.

We explore kinetic-constraint induced thermodynamic phase transition in the cubic lattice, employing the Fredrikson-Anderson spin model with hyperparameter $K=2$ as a representative kinetic system. Each lattice site may flip its binary occupation state if at most one of its six nearest neighbors is currently occupied. The whole set of microscopic configurations that are kinetically connected with the fully empty one is described by an equilibrium partition function with a single global constraint, that is, the occupied sites do not form closed loops but instead organize into different tree components in the lattice. We discover a continuous thermodynamic gas–crystal phase transition in the cubic system and determine the critical chemical potential $\mu^* \approx -3.252$, at which the occupied sites of the equilibrium tree-packing configurations start to prefer one of the two nested cubic sublattices. This thermodynamic phase transition is absent in the two-dimensional square lattice.

We introduce an incidence-based random walk on the edges of a random two-dimensional simplicial complex with a complete $1$-skeleton and independently retained triangular faces. The dynamics combine two transport channels, one mediated by vertices and the other by triangular faces, through an effective transition operator controlled by a mixing parameter $q$. This construction isolates the effects of higher-order connectivity without modifying the underlying pairwise support of the walk. We characterize the model through structural observables, spectral relaxation, stationary localization, and first-passage transport. Our results show that partial face retention generates heterogeneous higher-order connectivity, giving rise to a pronounced transport bottleneck at intermediate face densities. In this regime, the second-largest eigenvalue modulus, the inverse participation ratio of the stationary distribution, and the mean first-passage time all exhibit non-monotonic behavior, reaching their largest values at intermediate face densities. The corresponding first-passage-time distributions reveal an enhanced probability of unusually long trajectories. Together, these results establish a simple framework for investigating how heterogeneous higher-order connectivity reshapes spectral and transport properties beyond pairwise network dynamics.

Traveling waves are fundamental asymptotic structures in nonlinear physical systems. While their connection to self-similarity is recognized, their renormalization-group (RG) status remains elusive. We extend a recently developed unified RG framework for nonlinear PDEs to traveling-wave solutions, using Burgers' and KdV equations as paradigmatic examples. By employing a logarithmic transformation, we map traveling waves onto asymptotically self-similar solutions, allowing for a systematic RG treatment. Our analysis reveals a striking departure from the standard RG paradigm: for traveling waves, scale invariance uniquely forces the field's scaling dimension to vanish (A=0). This vanishing dimension implies that the RG transformation rescales space and time while leaving the field magnitude unchanged. Consequently, all analytic perturbations become scale-invariant, eliminating the conventional classification into relevant and irrelevant structures. While classical shock-wave and soliton solutions emerge as stationary RG fixed points, the mechanism for universality class formation - the progressive elimination of irrelevant structures - is fundamentally absent. Traveling waves thus represent a unique class of RG fixed points without universality classes. This finding establishes a crucial distinction between these two concepts and provides a rigorous theoretical basis for why traveling waves exhibit strong memory of initial conditions and system parameters.

How a quantum state responds to small parameter changes underlies state distinguishability, many-body response, and metrological sensitivity. The Pauli probability spectrum provides a natural description of many-body quantum states, but it is not evident how much of this response survives in the corresponding classical distribution. Here we show that, for pure states, the complete labeled Pauli distribution retains the full local metric of the pure-state manifold, reproducing the quantum Fisher metric up to a fixed normalization. This correspondence has a direct measurement realization: preparing a state together with its complex conjugate and performing pairwise Bell measurements between corresponding degrees of freedom converts the quantum response into an ordinary classical distribution without losing any of the sensitivity available in the two inputs. The readout is fixed, factorizes into local pairwise measurements even for strongly entangled many-body states, and preserves the response along all parameter directions simultaneously. We trace this correspondence to the reality of the underlying operator amplitudes and show that the same mechanism extends beyond qubits. When the correspondence fails, we identify explicitly where the missing information resides: part of the response can remain hidden in phases for identical-copy and complex-coordinate readouts, while mixed states develop transverse operator-space motion that is invisible to the Bell probabilities. These results provide a direct link between Pauli/Bell statistics, many-body response, nonstabilizerness, and quantum geometry.

Gutzwiller-projected Bardeen–Cooper–Schrieffer (BCS) wave functions of Abrikosov fermions are widely used to describe quantum many-body states. Taking the one-dimensional transverse-field Ising model as an example, we exactly embed any even-parity spinless fermionic Gaussian state representable as a paired exponential in the chosen particle basis into a projected BCS state of spinful Abrikosov fermions. The construction provides controlled initial states for variational Monte Carlo studies of nonintegrable models.

Let $\mathsf{d}\geq1$, $0<\mathsf{s}<\mathsf{d}$, and $N\geq1$. We prove that the optimal fixed-particle-number constant $\Lambda_N(\mathsf{s},\mathsf{d})$ in the Riesz Lieb–Oxford inequality is attained and that these constants are strictly increasing in $N$. The proof combines grand-canonical concentration–compactness with a strict one-particle extension. After recentering, a limiting plan arising from a maximizing sequence may assign positive probability to several particle numbers and hence be grand-canonical. A strict $N$-particle completion excludes this case, while the inequalities $\Lambda_N>\Lambda_k$ for $k<N$ exclude limits with a fixed lower particle number. Once attainment at particle number $N$ is known, the compact-support theorem of Di Marino and Lelotte arXiv:2607.11440, valid for all $0<\mathsf{s}<\mathsf{d}$, permits a non-product one-particle extension and yields $\Lambda_{N+1}(\mathsf{s},\mathsf{d})>\Lambda_N(\mathsf{s},\mathsf{d})$. Together, these implications close an induction beginning at $N=1$.

Tensor networks are powerful formats for compressing large-scale data. However, their application to general data processing has been limited by the difficulty of performing nonlinear operations. Here, we introduce iterative tensor network transformations (ITNTs), a general algorithmic framework for the element-wise evaluation of elementary and nonlinear filtering functions on data encoded as tensor trains (TTs), a class of tensor networks. Our approach operates entirely in the compressed domain, enabling efficient computation on exponentially large datasets while maintaining a controlled computational cost. We demonstrate its power in two key areas: (I) evaluating highly nonlinear elementary and filtering functions on a 3D reactive flow field, enabling high-fidelity reaction rate computation and region filtering, and (II) finding extrema in complex optimization problems, such as solving Max-SAT instances on spaces up to $2^{70}$ configurations. These results establish ITNT as a foundational tool that provides tensor network methods with the capability for general-purpose data science and large-scale optimization.

The solar wind is a turbulent, weakly collisional plasma characterized by non-Gaussian fluctuations, long-range correlations, and multifractal dynamics. We investigate the long-term evolution of these properties using hourly proton density measurements obtained directly by the Wind spacecraft over 1995–2025. The use of a single-spacecraft dataset provides an independent test of previous results derived from the multi-spacecraft OMNI database. The three components of the nonextensive $q$-triplet are estimated within one-year sliding windows shifted monthly: $q_{stat}$ from the distribution of density increments, $q_{rel}$ from the decay of the autocorrelation function, and $q_{sens}$ from the multifractal spectrum. Their mean values, $q_{stat}=1.71\pm0.07$, $q_{rel}=4.62\pm0.52$, and $q_{sens}=-0.45\pm0.27$, confirm the persistent presence of heavy-tailed statistics, slow relaxation, and weakly chaotic multifractal dynamics. The parameters nevertheless exhibit distinct temporal variability and relationships with solar activity. The Fourier spectrum of $q_{stat}$ contains a dominant period of approximately $10.1$ years, while its correlation with the sunspot number is positive and moderate ($r=0.611$). Correlation and mutual-information analyses show that $q_{stat}$ is primarily associated with solar proxies, whereas $q_{sens}$ displays stronger relationships with geomagnetic indices and $q_{rel}$ exhibits weaker dependencies. An anomalous enhancement of $q_{stat}$ around 2004 coincides with a sequence of intense interplanetary disturbances, although possible effects related to Wind's orbital transition must also be considered. These findings demonstrate the robustness of the nonextensive description and show that the statistical and dynamical properties of solar wind proton density show evidence of modulation by solar activity.

A long-standing obstacle in quantum turbulence has been the difficulty of sustaining robust statistical steady states, preventing unambiguous identification of universal vortex organization and kinetic scaling. We construct such a steady state in two-dimensional holographic superfluid turbulence by continuous Landau-instability driving, sustaining ${\sim}2500$ vortices free from transient artifacts. The topological charge structure factor $S_c(k)$ reveals Class I disordered hyperuniformity with $S_c(k)\propto k^{\alpha>1}$ as $k\to0$, where $k$ is the wavenumber. This constitutes the strongest long-range order of its kind and its first observation in a strongly driven, far-from-equilibrium quantum fluid with topological defects as the organizing principle, establishing a novel non-equilibrium vortex phase. Exploiting this platform, we resolve the scaling controversy: the apparent $k^{-5/3}$ signature in the kinetic energy spectrum is a narrow crossover between the $k^{-1}$ single-vortex and $k^{-3}$ core regimes, not a genuine Kolmogorov inertial range. The real-space second-order structure function provides decisive evidence via $S_2(r)\propto \ln r$ where $r$ is the spatial separation, with no $r^{2/3}$ Kolmogorov scaling, ruling out a true inertial cascade. These findings reveal that strongly coupled quantum turbulence lacks an inverse cascade due to the absence of macroscopic Onsager clusters, demonstrating energy transport fundamentally distinct from weakly coupled superfluids.

We study interacting scalar quantum field theories in anti-de Sitter (AdS) space using a tensor-network approach based on matrix product states. We develop methods for extracting low-lying boundary spectra from global-AdS energy levels, probing bulk criticality through finite-size scaling in the AdS radius, and identifying conformal boundary conditions. Applying these methods to scalar $\phi^4$ theory in $\mathrm{AdS}_2$, we compute the lowest non-trivial $\mathbb{Z}_2$-odd and even boundary scaling dimensions non-perturbatively. We then locate the bulk $\mathbb{Z}_2$ symmetry-breaking transition and extract critical exponents and central charge consistent with the 2D Ising universality class. At the critical point, we determine the low-lying boundary spectrum and use it to identify the $\mathbb{Z}_2$-preserving free/ordinary Ising conformal boundary condition, thereby characterising both the bulk and boundary universality classes.

We study the spread complexity of the infinite-temperature thermofield double state in large-$N$ random matrix theory and investigate the physical meaning of its Lanczos coefficients $b_n$. The leading density of states defines a family of orthogonal polynomials whose recursion coefficients coincide with the Lanczos coefficients of the associated Krylov dynamics. Starting from the Coulomb-gas equation, we derive a pair of nonlinear relations for these coefficients, which we call the Lanczos equations. For normalizable one-cut ensembles, the Lanczos coefficients approach constants at large Krylov index, rendering the asymptotic Krylov chain translationally invariant and the late-time growth of spread complexity linear, with the growth rate given by the spectral average of the group velocity obtained from a Bloch-wave analysis. For an even potential, we further show that the difference between consecutive squared Lanczos coefficients, $b_{n+1}^2-b_n^2$, is the generating function for two-legged maps whose marked legs are separated by the exact geodesic distance $n$. Consequently, the spread complexity acceleration operator equals twice the geodesic generating operator. We illustrate these results in the quartic matrix model, where the expansion in the quartic coupling counts tetravalent planar maps, and in the double-scaled Sachdev–Ye–Kitaev model, where the auxiliary Hilbert space can be identified with the physical chord Hilbert space.

We propose a three-terminal thermal amplifier based on a Sierpinski-gasket Aharonov-Bohm interferometer, where the third (base) terminal is realized as a floating Buttiker probe that acts as an engineered dissipative reservoir, exchanging energy with the conductor while carrying no net charge current. Using the nonequilibrium Green's function formalism, we demonstrate that the interplay of quantum coherence and engineered dissipation gives rise to giant, magnetic-flux-controlled thermal amplification, whereas purely coherent transport exhibits little or no amplification. We show that the amplification originates from a flux-induced cancellation of the energy-resolved thermal response of the base terminal, causing its differential heat current to vanish while finite heat currents continue to flow through the emitter and collector terminals. As a result, the thermal gain diverges without requiring resonant transmission. This interference-driven cancellation gives rise to an emergent thermal transparency, closely analogous to electromagnetically induced transparency in optical systems, where destructive quantum interference suppresses the thermal response of the base reservoir while maintaining finite heat transport through the remaining terminals. Our results establish the interplay of engineered dissipation and quantum interference as a powerful mechanism for controlling heat flow and realizing high-performance thermal amplifiers in mesoscopic conductors.

We determine the distribution of fidelity susceptibility for chaotic eigenstates at the spectral edge of Gaussian random-matrix ensembles. Previous work showed that, in the unitary class, the characteristic susceptibility scale of edge states grows as $D^{1/3}$, rather than proportionally to $D$ as in the spectral bulk, reflecting Airy-edge level rigidity. Extending a determinant-based framework introduced for bulk states, we derive the universal edge distributions for both the orthogonal and unitary ensembles. The two symmetry classes share the scaling variable $g/D^{1/3}$ and exhibit a symmetry-dependent cubic suppression of small susceptibilities, while their algebraic large-$g$ tails reflect the corresponding symmetry-dependent level repulsion. Although eigenvector statistics retain their random-matrix form throughout the spectrum, edge rigidity makes low-lying chaotic states parametrically less sensitive to generic perturbations than bulk states. Our results establish universal, symmetry-dependent spectral-edge fidelity-susceptibility statistics in systems whose chaotic dynamics extends down to the ground state.

We perform a large-$x$ asymptotic analysis of the Fredholm determinant of an integrable integral operator with generalized sine kernel, where $x$ controls the strength of the oscillations along the integration contour of the operator and will play the role of the distance variable in applications to the correlation functions of integrable quantum systems. Our generalized sine kernel involves a number of functional parameters that will allow us to adapt it to the analysis of the dynamical correlation functions of the Lieb–Liniger model at finite temperature and for all positive values of the coupling constant. It will also allow us to consider a class of equilibrium correlation functions that are governed by generalized Gibbs ensembles. Our work is based on the analysis of a matrix Riemann–Hilbert problem that is canonically connected with our integrable integral operator.

A self-contained statistical-mechanics treatment of a single quantum harmonic oscillator is presented, whose frequency $\omega$ is drawn from a folded Gaussian distribution: $\omega=|\xi|$ with $\xi\sim\mathcal{N}(\mu,\sigma^2)$. The exact integral representations for the partition function, internal energy, free energy, heat capacity, and entropy are derived, and analytic approximations are given in two complementary limits—small variance ($\sigma\ll\mu$) via a cumulant expansion, and the zero-center case ($\mu=0$) via low-frequency asymptotic analysis. The model is extended to $N$ independent oscillators, where the heat capacity is shown to be extensive with self-averaging fluctuations $\propto N^{-1/2}$, and finally to a disordered oscillator lattice, where the folded-Gaussian kink at $\omega=0$ produces a soft-mode infrared tail. For a single isolated oscillator with $\mu=0$, both $C$ and $S$ vanish linearly at low $T$. In the lattice case, the van Hove factor converts this to a $T^d$ power law. The oft-quoted “third-law violation” for disordered phonons is here shown to be a spectral property—the absence of an energy gap and a power-law freeze-out—driven by the single-site distribution kink rather than by a genuine Lifshitz tail (which requires rare large-scale spatial fluctuations). The folded Gaussian thus serves as a minimal benchmark for soft-mode disorder thermodynamics.

Experiments have revealed that collective strong coupling in optical cavities can drastically alter the conductivity and dielectric properties of molecular ensembles, or even trigger abrupt phase transitions (in Rayleigh scattering or dispersion force driven conformational equilibrium). Until now, the underlying physical mechanism has remained unknown. A recently proposed theory attributes these collective effects to cavity-induced electron correlations that share properties of the known spherical Sherrington-Kirkpatrick model of a spin glass. As a consequence, entropic effects can trigger a phase transition in the inter-molecular electron correlations that could potentially explain the above experiments. In the following work, we derive analytic expressions for the correlation (free-)energy-induced polarizability changes, which reveal that under certain conditions collective strong coupling can even render our molecular ensemble metallic by entropically ionizing collectively degenerate molecular orbitals. Our results are a first major step towards a holistic theory of cavity-mediated electron correlation effects.

We find no evidence of critical scaling in the Schelling segregation model, in either the Moore neighborhood or its dense-spectrum extension to Chebyshev radii up to $r_0 = 6$ ($k = 168$ neighbors). On periodic grids up to $L = 320$ with 50 trials per point (> 12,500 runs), every finite-size scaling diagnostic in the Moore baseline fails: the per-$L$ $T_c$ does not drift, Var$(S) \sim L^{-2.02 \pm 0.09}$ matches trivial averaging, $\gamma/\nu \approx 0$, and the scaling collapse never reaches a finite optimum. The 8-site Moore neighborhood restricts satisfaction to ratios $j/k$ with $k \leq 8$, giving $S(T)$ a staircase structure with 23 rational thresholds; discreteness alone does not forbid criticality (cf. the Ising model), but the scaling evidence rules it out empirically. A branching-ratio calculation predicts subcritical cascades of mean size $1/(1-R)$ and is validated by perturbation experiments to within 15%; the multiscalar dissimilarity length stays finite across the transition. The dense-spectrum extension strengthens the negative verdict: across $r_0 \in {3,4,5,6}$ on $L \in {40,80,160}$ the Binder cumulant has no $L$-curve crossing and the per-$L$ $T_c$ drift is monotonic and unsaturated; at $r_0 = 4$, extending to $L = 320$ gives $\alpha = -2.70$, below the critical boundary $\alpha = -2$, dissolving an apparent $\alpha = +0.81$ signal visible only on $L \in {40,80}$. The mechanism is the absence of long-range correlation in equilibrium plus deterministic high-$k$ dynamics, not the staircase structure. With a Beta-distributed heterogeneous tolerance, the intolerant tail drives segregation even at moderate population-average tolerance. The staircase theorem and cascade mechanism together account for the Schelling transition without invoking critical phenomena.

Understanding the stochastic evolution in complex networks is a central challenge across physics, biology, engineering, social science, and finance. The most consequential macroscopic events, like cascading failures in communication networks, widespread epidemic outbreaks, and rapid shifts in societal opinions, often emerge from a confluence of rare, localized stochastic processes and need to pass certain bottlenecks. Standard forward-time simulation algorithms like the Gillespie method are inefficient for the investigation of such phenomena due to catastrophic rejection rates. Advanced rare-event techniques like splitting methods and transition-path sampling often suffer from kinetic trapping, path degeneracy, genealogical correlations, or critical slowing down when applied to complex heterogeneous networks. We propose to overcome this challenge by establishing a novel technique called conditional-path Monte Carlo (CPMC), inspired by loop algorithms from equilibrium condensed-matter physics. By employing non-local updates on spacetime clusters without rejections, CPMC generates a Markov chain of trajectories that all strictly respect the targeted macroscopic boundary conditions like the occurrence of a massive network failure. We demonstrate the framework's potential by performing a simple risk factor analysis for rare large-scale epidemic outbreaks in SIS dynamics on kinship networks.

Thermodynamic stability and causality impose fundamental constraints on the equation of state (EoS) of nuclear matter. Verifying these constraints conventionally requires calculating quantities such as the specific heat, baryon-number susceptibility, and speed of sound, which can become computationally expensive when many candidate EoSs must be examined. We investigate whether the normalized pressure surface, $Q(T,\mu_B)=P(T,\mu_B)/T^4$, alone contains sufficient information to determine the physical admissibility of an EoS. We develop a supervised convolutional neural network (CNN) that uses only this pressure representation to classify EoSs as physically admissible or inadmissible. The network is provided with training labels obtained from direct thermodynmaic stability and causality check and its does not get any information about the parameters of the underlying EoS framework. For EoSs generated within an Ising-mapping framework, the model achieves $97.65%$ accuracy on unseen test data. Applied independently to EoSs from a distinct holographic framework, it achieves perfect classification of the test set. These results show that pressure surfaces contain geometric signatures of thermodynamic stability and causality violations that can be learned directly by a CNN. Because the classifier relies only on the pressure surface, it avoids evaluating higher-order thermodynamic observables during inference and is largely independent of the EoS-generation framework. When the pressure surface is supplied as a two-dimensional array, the machine-learning validation is approximately 20 times faster than direct validation. Our results establish a fast, framework-independent approach for identifying physically admissible EoSs directly from their pressure surfaces.

We compute the dynamic critical exponent $z$ of the Yang–Lee edge singularity in relaxational dynamics using perturbative renormalization-group methods to the three-loop order. The calculation combines diagram reduction, analytic two-loop evaluation via parametric integration with hyperlogarithms, and numerical evaluation of three-loop integrals using the Sector Decomposition method. The perturbative series obtained is resummed using Padé and Padé-Borel-Leroy methods to produce estimates of $z$ in various spatial dimensions. The resulting values are consistent with previous perturbative and functional renormalization-group calculations.

We show that the Hodge-de Rham decomposition of the Berry curvature organises the transport of a Bloch band and its fluctuations within a single geometric structure. Splitting the curvature into $L^2$-orthogonal harmonic, exact, and co-exact sectors yields a dictionary for both moments of the current. In the mean response the harmonic sector carries the topological anomalous-Hall conductivity, the exact sector the Fermi-surface geometry and the antisymmetric Berry-curvature dipole of polar metals, and, in three dimensions, the co-exact sector the chiral anomaly, quantised by the Weyl-node charges. In the fluctuations, described by a particle-conserving stochastic Boltzmann equation constrained by the fluctuation-dissipation theorem (FDT), the harmonic sector is silent, so topological transport is noiseless, while the field-driven noise is sourced by the geometric sectors (solely the exact sector in two dimensions); current-noise spectroscopy therefore separates global band topology from local band geometry. We prove that the harmonic null-space protection is dimension-independent, and we settle the remaining sector: the co-exact (monopole) sector carries no conservation law and, under the thermal sampling measure, mixes with the exact sector at $\mathcal{O}(1)$, so it furnishes no clean noise observable. The separation the noise provides is therefore two-way, topology versus geometry, in both two and three dimensions.