Papers

We investigate the structure and dynamics of a polymer in a fluid containing mobile spherical colloidal crowders of radius $R$. We compare and contrast the behavior with Langevin dynamics (LD) and lattice–Boltzmann molecular dynamics (LBMD), the latter incorporating long-range hydrodynamic interactions. Both the colloid size relative to the monomer radius $r$ and the volume fraction $\phi$ are varied to determine how crowding modifies polymer behavior. Increasing volume fraction induces polymer compaction, with the mechanism strongly dependent on the size ratio $R/r$. Small colloids primarily modify the short-wavelength polymer conformation, causing self-avoiding-walk-like behavior to persist to shorter length scales, whereas large colloids reduce the effective long-wavelength Flory exponent, indicating degraded solvent quality consistent with a confinement-blob picture. Polymer diffusion exhibits distinct behavior in LD and LBMD. In LD, diffusion decreases rapidly and depends strongly on $R/r$; a phenomenological scaling involving $\ln(1+R/r)$ captures this size dependence, and additional scaling with $R_g$ reduces scatter, indicating polymer-scale correlations induced by crowding. In contrast, LBMD diffusion follows an effective-medium-like exponential dependence on concentration, governed by hydrodynamic coupling. Rouse-mode analysis identifies three regimes: scaling breakdown at low volume fraction, Zimm-like behavior at intermediate density in both LD and LB, and at high density hydrodynamic screening in LB with confinement-dominated dynamics in LD.

We study a class of Hamiltonians with a structure that we call "dynamical splitting": the Hamiltonian terms can be divided into two sets acting on the same degrees of freedom such that every term in one set commutes with every term in the other, although terms within either set do not all commute. This structure yields an algebraic duality to effective degrees of freedom on which the two parts of the Hamiltonian act disjointly, enabling exact diagonalization on lattices with approximately twice as many spins as usually accessible. We exploit it in the "chiral XYZ model", a geometrically frustrated spin-$1/2$ model on the triangular lattice which was previously introduced as a special limit of a Majorana-Hubbard model. This model also possesses anticommuting noncontractible line symmetries, which enforce an exact, topology-dependent degeneracy between locally indistinguishable states. We first study a $\mathbb{Z}_N$ clock generalization and find, at large $N$, a gapless ground state with three subsystem-symmetry-protected nodal lines. Exploiting dynamical splitting and the subsystem symmetries, we carry out exact diagonalization of the $N=2$ model on lattices up to $9\times9$ spins. The many-body gap and bipartite entanglement provide strong evidence for a gapless state consistent with the large-$N$ nodal structure: the entanglement scales as $L\log L$ and exhibits $1+1$-dimensional CFT-like chord scaling on cylinders. Finally, we study instabilities and proximate phases. In particular, we find evidence that a subsystem-symmetry-preserving deformation drives a finite coupling transition to a gapped phase with $\mathbb Z_2 \times \mathbb Z_2$ topological order.

Work extraction from nonequilibrium systems is a major challenge across biological, chemical, physical, and engineering systems. Idealized protocols generally require a quasistatic relaxation stage in which the Hamiltonian is gradually adjusted through a continuum of intermediaries. Here, we consider protocols restricted to a finite number $N$ of intermediary Hamiltonians, consisting of a sequence of quench-relax steps. We determine the sequence of quenches that minimizes the dissipated work, which can be expressed in terms of a recurrence involving the Lambert function. The optimal sequence converges to the Fisher-Rao geodesic, saturating known leading-order dissipation bounds at large $N$. We obtain lower bounds on work extraction from a nonequilibrium distribution as a function of its Fisher-Rao distance to equilibrium. We extend and apply the framework in two simple models: (i) an optical trap experiment, showing that the optimal intermediary distribution can be bimodal even for unimodal initial and final distributions, and (ii) an enzyme-catalyzed reaction, showing that that accounting for relaxation time in addition to dissipation can favor barrier-lowering.

Relaxation toward equilibrium is usually accelerated by modifying the environment or by cooling a system further from equilibrium. Here we introduce a distinct strategy: thermalization packets, auxiliary systems prepared in advance and later coupled to a target system to accelerate its relaxation toward a prescribed thermal state. Thus, thermalization packets trade preparation effort for reduced waiting time. When the objective is cooling, we colloquially refer to such packets as ice cubes. Unlike ordinary coolants, thermalization packets are characterized not only by their temperature or heat capacity, but also by their microscopic preparation. We define perfect and optimal packets by their ability to suppress the slowest relaxation mode of the coupled dynamics: perfect packets eliminate it entirely, while optimal packets minimize its amplitude. We show that, under generic conditions, perfect packets exist among thermal preparations near equilibrium. Surprisingly, for asymptotic relaxation, the optimum among thermal preparations is generally not the coldest packet: cooling the packet beyond the slow-mode-cancelling optimum restores a nonzero slow mode and can therefore slow relaxation, yielding a packet analog of the Mpemba effect. We demonstrate the concept in exactly solvable Metropolis dynamics, a minimal two-qubit model, and a boundary-coupled interacting Ising-spin system. We also extend the framework to packets optimized for finite readout times. Finally, we show that the perfect-packet contour can connect the trivial bath-equilibrium point to a nontrivial strong Mpemba or strong inverse-Mpemba point.

Conformal invariance is expected to be an emergent property of many systems in their critical regime. However, approximation schemes generically spoil this property. This is in particular the case of the derivative expansion, a widely used approximation scheme in the framework of the functional renormalization group. In this article, we consider Ward identities associated with conformal invariance in the 3-d Ising universality class with truncations at order 4 (next-to-next-to-leading order) in the derivative expansion, with $Z_2$ invariant composite operators. Our results confirm that the regulating functions which yield a small breaking of conformal invariance also present a small sensitivity of the universal critical exponents with the choice of this regulating function. We also show that, in the vicinity of regulator-parameter values for which the conformal constraints are best satisfied, the breaking of conformal invariance reduces as the order of the derivative expansion is increased, providing a new indication of the convergence of this approximation scheme.

Optimal control helps guide our understanding of stochastic thermodynamics, leading to universal properties and geometric formulations. Among the initially surprising properties of optimal control, not only discrete jumps but delta function kicks have been shown to be necessary to minimize dissipation in specific example systems. Using a short-time approximation, I show that delta-function kicks are universally optimal for minimizing dissipation in inertial stochastic systems, including active and quantum dynamics under general constraints. Fundamentally stemming from basic kinematics, delta-function kicks are required to achieve linear scaling of work with short protocol durations compared to the quadratic scaling without the kicks. This implies a diverging (infinite) ratio of saved work in the short-time limit.

The entropy production rate (EPR) quantifies irreversibility of a nonequilibrium steady state, yet standard formulas obscure how a complex interaction network generates it. For multivariate Ornstein-Uhlenbeck dynamics on such networks, we express the EPR as a quadratic form in antisymmetric matrices measuring the nonreciprocity of aggregate directed walks at every length, and, equivalently, as two weighted-walk quantities: pairs of directed walks sharing both endpoints, and directed closed walks. For diagonalizable interactions, an exact correspondence translates these walk quantities into eigenvalues and biorthogonal eigenvector overlaps. Across dense, sparse, and deep acyclic random interactions satisfying matched-walk conditions, the mean EPR per node universally follows the square-root law $\phi_*(g)=1-\sqrt{1-g^2}$, where $g \in [0,1)$ parametrizes the interaction strength. Deep acyclic interaction matrices are nilpotent, with all eigenvalues fixed at zero for every $g$, yet, as their depth increases, their mean EPR per node approaches $\phi_*(g)$. Thus, the square-root law arises from directed walk properties, rather than from a shared spectral density or specific network topology.

Geometry of quantum states is a fundamental research area with applications ranging from topological materials in condensed matter to variational algorithms in quantum information. Due to their relative simplicity, pure states are often studied, while mixed states are generally needed, for instance to have nonzero temperatures or other statistical mixtures. Mixed-state geometry, however, is much more challenging and has so far lacked any overall structure that relates distance and curvature, like the Kähler structure does for pure states. This work introduces that missing structure. We show that it has the physical meaning of fluctuation-dissipation—by identifying distance with fluctuations and curvature with linear response—and becomes the known structure for pure states, but is non-Kähler otherwise. This paints a simple picture that unifies fluctuation-dissipation and geometry of quantum states. It also applies on parameter spaces, as encountered in condensed matter or estimation theory. Our picture implies that the geometry contains all linear responses and fluctuations, proves the usual fluctuation-dissipation relation, explains that quantum geometry is present in any sum rule, and allows one to geometrically characterize generic transport behaviors.

We experimentally investigate how symmetry-protected topological order in a one-dimensional cluster state is transformed by measurement and decoherence in a five-qubit superconducting array. We first characterize the state's nonlocal string order and show that controlled dephasing selectively suppresses one symmetry sector while leaving the other robust, consistent with average symmetry-protected topological order. We then measure one sublattice in a tunable basis and show that the remaining qubits are driven between a long-range-entangled GHZ state and a paramagnetic state. When the measurement record is discarded, the conventional long-range correlator vanishes while a nonlinear fidelity correlator remains finite, providing a finite-size signature of strong-to-weak spontaneous symmetry breaking. These experiments demonstrate how conditioning, averaging, and decoherence reveal distinct manifestations of order encoded in the same underlying cluster state, and establish a superconducting-circuit setting for probing mixed-state symmetry and topology.

The Johnson-Nyquist theory is commonly implemented by representing a conductor as a collection of independent local thermal-noise sources whose strength is determined by the local temperature. Whether this local-noise representation remains valid for electrically coupled conductors maintained at different temperatures has received comparatively little attention. We investigate this question by means of microscopic two-dimensional simulations of interacting charge carriers in conducting wires capacitively coupled. The model reproduces Ohm's law, the equilibrium Johnson noise, and vanishing correlations between detached wire segments when both wires are at the same temperature. However, when the wires are held at different temperatures, finite correlations develop between the electromotive forces generated in distant segments, leading to systematic deviations of the Johnson temperature inferred from the local-noise picture. The effect persists although the microscopic particle interactions are short-ranged and the two wires interact only through the capacitive coupling. These results suggest that the independent-local-source representation of thermal noise may not remain valid in electrically coupled nonequilibrium conductors.

Electromagnetic fluctuations can transfer not only energy but also angular momentum, leading to forces, torques, heat currents, and friction in out-of-equilibrium setups. In enclosing configurations, we show that if at least one of two objects is rotationally symmetric, the torque is bounded by heat transfer, since both arise from photon transfers with angular momentum $\hbar n$ and energy $\hbar\omega$. With only one object assumed to be rotationally symmetric, it may be possible to obtain a nonzero torque with reciprocal media, but nonreciprocal media are required to break the symmetry between $n$ and $-n$ and produce a nonzero torque if both objects are rotationally symmetric. We then specialize to concentric cylinders with a nonreciprocal dielectric response and use Rytov fluctuational electrodynamics to express heat transfer and torque in terms of an angular-momentum-resolved flux density, $\Phi_n(\omega)$. We also analyze the conditions for stable levitation of the inner cylinder using the proximity force approximation, in the process obtaining a new analytic formula for the normal Casimir force between dilute plates at different temperatures. Finally, to find the extracted work in a contactless engine setup, we compute the fluctuation-induced friction for a slowly rotating inner cylinder, and we find a bound between torque, friction, and heat transfer. Due to this bound, the efficiency of the heat engine remains bounded by the Carnot limit.

The design of disordered point patterns with desirable properties is an exciting and ongoing research endeavor, with applications ranging from materials to computer science. A successful approach in recent years has been the optimization of point patterns through a loss function that enforces properties in their Fourier-space representation. Yet, these methods have so far strictly been limited to flat Euclidean space, precluding their use in the contexts of coatings of curved surfaces for photonics, or of sampling of curved manifolds for instance. We introduce FaSHIoNPOp, an algorithm that relies on fast non-uniform spherical harmonics transforms, to enforce pair correlations in point patterns on the sphere with an $O(N \log N)$ complexity in $N$ the number of points. Having demonstrated its performance, we showcase applications of FaSHIoNPOp, ranging from the generation of hyperuniform structures on the sphere for sampling and physical applications, to the design of gyromorphs (disordered structures with maximal scattering power at a given frequency) on the sphere. We additionally show that FaSHIoNPOp can be combined to both global constraints like centrosymmetry, with applications to the design of more isotropic $3d$ gyromorphs, and local real-space constraints like pair repulsion. Our work paves the way for optimal sampling and coating design on curved manifolds, with many applications across physics, materials and computer science.

Nucleation is a key rate-limiting process in phase transition and phase separation. Recent studies highlight a significant discrepancy between experimentally measured nucleation rates and theoretical predictions, particularly when dynamic structural reordering occurs along multi-step pathways. To bridge this gap, we develop a multi-shell model with a space-time-dependent order-parameter field to describe the reordering-nucleation process, where structural reorganization couples with the early growth of condensed clusters. Through stochastic simulations, we track the time-resolved evolution of heterogeneous structural order inside growing clusters. Path analysis of the first-passage problem in early-stage nucleation demonstrates that shifting the reordering rate alters the nucleation rate by several orders of magnitude. Furthermore, as the coupling strength increases, the relationship between the mean first-passage time and reordering susceptibility shifts from monotonic to non-monotonic, exhibiting a turnover effect. We quantitatively rationalize these behaviors with an effective nucleation barrier that accounts for non-equilibrium properties. Our findings elucidate the mechanisms behind multi-step nucleation and offer a predictive framework for future studies.

We study the equilibrium phase behavior of a fluid confined in a slit made from two patterned walls. Shearing the walls frustrates the fluid, due to a competition between capillary condensation and interface delocalization, forcing the formation of bridging phases with different pinning properties. This leads to an unusually rich phase diagram, displaying first-order and continuous phase transitions, depending sensitively on the slit width and shear. Generalized Kelvin equations determine the phase boundaries, while the bridging phases are characterized by large correlation lengths, predictions for which are tested using a microscopic density functional model.

Abrupt transitions between rest and motion can render the standard Newtonian description – based on position, velocity, and acceleration – incomplete, requiring higher-order derivatives such as the jerk, the third time derivative of position. Here, we show that the interplay between activity and dry friction gives rise to robust jerk-dominated dynamics in self-propelled particles: the particle speed increases quadratically with time under an active force, in contrast to the linear growth expected for conventional Newtonian dynamics. We demonstrate this behavior analytically, numerically, and experimentally using active vibrobots self-propelling on a vertically vibrating plate at low vibration amplitudes, where surface asperities generate dry friction and, thus, give rise to jerky motion when combined with activity. Our results establish dry friction as a simple mechanism for realizing higher-order dynamics in active matter and suggest that jerky dynamics may arise broadly in nonequilibrium systems with frictional contacts.

In this work we present a large-deviations approach to the calculation of the canonical partition function for free bosons. Three-dimensional Bose-Einstein condensation is studied in the fixed-density ensemble as a function of the dimensionless density $\varrho = \rho \lambda_T^3$, with $\rho=N/L^3$ the standard particle density, $\lambda_T$ the thermal wavelength, $L$ the linear size of the box and $N$ the total number of particles. A large-deviations approach in terms of the dimensionless parameter $\ell=L/\lambda_T$ allows us to provide exact asymptotic estimates of the canonical partition function both above and below the critical density $\varrho_c$ for Bose-Einstein condensation. We show how this approach allows to explicitly account for finite-size effects and how it fully captures the first-order aspects of the transition, allowing us to explicitate its driving mechanism in terms of the competing probabilities of normal and condensed phases. The proposed large-deviations approach allows then to obtain in all regimes explicit and simple analytical expressions, at the leading order in the large parameter $\ell$, for both the average fraction of particles in the ground state, the condensate fraction $\langle n_0(\varrho) \rangle = \langle N_0(\varrho) \rangle/N$, and for its fluctuations, $\sigma_0(\varrho) = \sqrt{\langle N_0^2(\varrho)\rangle - \langle N_0(\varrho)\rangle^2}/N$, retrieving for instance the anomalous scaling $\sigma_0(\varrho)\sim 1/V^{1/3}$ in the condensed regime, $\varrho > \varrho_c$. Our large-deviations asymptotic estimate, by analytically clarifying the mixed-order nature of Bose-Einstein condensation, allows then to reveal the similarity between this transition and other mixed-order transitions, as for instance the localization transition in the Discrete Non-Linear Schrödinger Equation.

We study the dynamics of the cumulants of the entanglement Hamiltonian in interacting integrable models following global quantum quenches. Building on recent results based on space-time duality, we show that these cumulants are exactly given by the cumulants of currents of suitable conserved charges evaluated in the macrostate selected by the initial state. This establishes a direct connection between entanglement dynamics and transport, providing a transport counterpart to the quasiparticle picture that successfully describes the evolution of the von Neumann entropy. In the free-fermion and conformal limits, our results reduce to the difference between the current cumulants carried by right- and left-moving excitations, recovering previously known expressions. In interacting integrable models, where a decomposition into independent right and left movers is no longer meaningful at the operator level, a similar structure survives at the level of the entanglement spectrum, yielding a unified description of entanglement Hamiltonian fluctuations across free, conformal, and interacting integrable systems.

In this work, we investigate quantum quenches in the two-leg Creutz model with long-range hopping, where the hopping amplitudes decay with distance as a power law characterized by an exponent $\nu$ and have a finite range $D$. We first obtain the exact solution of a generic two-band model in momentum space. This allows us to compute the Loschmidt amplitude and, consequently, the dynamical free energy $f(\texttt{t})$ of the two-band model. We also show how to determine the Yang-Lee Fisher (YLF) zeros by solving a nonlinear equation. We demonstrate that the two-leg Creutz model in momentum space is a special case of the generic two-band model. Using these results, we identify the non-analyticities in the dynamical free energy $f(\texttt{t})$ at critical times $\texttt{t}_{c}$. We find that the number of nontrivial critical times $N_{s}$ depends on both $\nu$ and $D$. In particular, we show that for small $\nu$ and large $D$ the critical times become increasingly dense, leading, in the appropriate regime, to non-analyticities at an increasingly dense set of times—similar to what was observed by Xavier and Hoyos [Phys. Rev. B, $\textbf{108}$, 214303 (2023)] in the Su-Schrieffer-Heeger (SSH) model with long-range hopping terms.

We show that stigmergic path formation emerges in a deformable environment through the interplay between environmental memory and geometrical crowding. Using experiments with robotic random walkers together with a minimal stochastic model, we demonstrate the onset of persistent self-reinforced transport pathways above a critical packing fraction $\phi_c$, where environmental memory enhances walker mobility. As the jamming transition $\phi_J$ is approached, increasing crowding progressively suppresses this transport enhancement despite the persistence of environmental memory. The resulting non-monotonic behavior reveals an optimal transport regime well below jamming. More generally, our work establishes how active agents can collectively build transport networks through purely mechanical interactions with a deformable substrate.

Exact sampling from the Boltzmann distribution of spin glasses remains an outstanding challenge: Markov chain Monte Carlo methods suffer from critical slowing down and metastable trapping, while modern neural autoregressive samplers such as variational autoregressive networks are approximate and, in the absence of exact reference samples, cannot be rigorously benchmarked. Here we present an exact autoregressive sampling algorithm for planar Ising spin glasses based on the Kac–Ward theory. Under the chain-rule factorization, sequentially fixing spins induces boundary-localized external fields, which destroy the zero-field structure required for exact evaluation. By encoding these fields with a planarity-preserving auxiliary spin construction, the conditional partition functions are mapped to an extended zero-field Ising model and exactly evaluated using the Kac–Ward determinant formula. The method generates strictly independent and identically distributed samples with exact normalized likelihoods at a computational cost of $\mathcal{O}(N^{5/2})$ for $N$ spins, thereby providing an exact baseline for benchmarking neural autoregressive samplers.

We study boundary free energies and half-space responses in nearest-neighbor disordered Ising models. First, we prove the existence of fixed-depth tangential pressure and identify its derivative almost everywhere with the limiting boundary response. Second, under quenched exponential boundary-response mixing, we prove Gibbs-state selection independence and exponential convergence of finite-depth pressures. We further show that uniform one-spin mixing yields DLR uniqueness and Gaussian normal localization, and verify the required mixing conditions whenever $(2d-1)\mathbb E\tanh(\beta\vert{}J\vert{})<1$. Finally, we establish an all-face surface limit in the bounded Dobrushin regime and provide counterexamples that delimit general surface and stiffness claims.

We investigate the cluster Ising chain with an additional nearest-neighbor interaction using tensor-network methods and a weak-coupling field theory. Without the interaction, the Jordan-Wigner transformation decomposes the model into a triplet of identical Majorana chains related by an exact $O(3)$ flavor symmetry. Their common mass vanishes at the $SU(2)_2$ Wess-Zumino-Novikov-Witten critical point with central charge $c = 3/2$ separating the symmetry-protected topological cluster phase from a ferromagnet. The interaction reduces $O(3)$ to its cyclic subgroup $C_3$, splitting the triplet into a singlet and a doublet whose gaps close separately, producing a critical bifurcation into Ising ($c = 1/2$) and Gaussian ($c = 1$) critical lines. A second ferromagnetic phase opens between these critical lines for repulsive interactions and a disordered phase for attractive ones. The Gaussian line then separates two Landau-incompatible ferromagnets, realizing a deconfined quantum critical line with emergent $O(2)$ symmetry, along which our independently extracted exponents vary continuously yet satisfy the parameter-free relation $\beta = (2\nu - 1)/4$ of the eight-vertex weak universality class. At stronger repulsion this line opens into an extended gapless floating phase with incommensurate algebraic correlations, entered through Berezinskii-Kosterlitz-Thouless transitions. All of these phases and the transitions between them are captured by the weak-coupling theory. Beyond its regime of validity, our simulations reveal a translation-symmetry-breaking antiferromagnet reached through first-order transitions.

Inspired by the chemical reaction network considered as the smallest system featuring a Hopf bifurcation and its reversible extension, we introduce an even more minimal reaction network that is thermodynamically consistent and exhibits autonomous oscillations under nonequilibrium driving. The model combines three features that are rarely realized simultaneously in compact oscillator networks: a chemically plausible structure restricted to uni- and bimolecular reactions, reversibility of such reactions, and analytical tractability. The system consists of three internal species coupled to two chemostatted species and still undergoes a supercritical Hopf bifurcation when a chemostat concentration is varied. To analyze the dynamics and thermodynamics near the onset of oscillations, we employ the mathematical technique of normal-form reduction, which allows obtaining a controlled irreversible approximation that preserves the leading phase-space structure of the full reversible network while enabling explicit calculations. This framework provides analytical access to the bifurcation structure and the leading contributions governing thermodynamic observables. Within this setting, we use the onset of oscillations to characterize the thermodynamic response of the system. In particular, we offer an analytical description of key thermodynamic quantities such as the semi-grand Gibbs free energy and the non-conservative work rate, which exhibit a kink-like discontinuity at the Hopf bifurcation. We thus provide an analytical description of a phenomenon previously characterized only through numerical simulations of more complex networks.

According to Purcell's scallop theorem, reciprocal single-degree-of-freedom shape deformations cannot achieve net propulsion in a viscous fluid. We show that this limitation is bypassed by thermal fluctuations in a two-parameter driven potential landscape. Formulating the stochastic shape dynamics via a Smoluchowski equation with position-dependent mobility $M_\mathrm{eff}(x)$, we utilize a generalized inverse operator to evaluate the slow-driving response. Cyclic modulation of the control parameters induces a non-zero Berry-Sinitsyn-Nemenman curvature $F_{12}(\bm{\theta})$, resulting in directed geometric propulsion. Simultaneously, the non-adiabatic excess dissipation is dictated by a Riemannian thermodynamic metric $g_{ij}(\bm{\theta})$. Our results provide a unified geometric foundation that bridges hydrodynamic friction, stochastic mechanics, and thermodynamic trade-offs in micro-swimmers.

We study long-range correlated Wigner-type matrices built from row-independent stationary Gaussian sequences. For exponentially decaying (AR(1)) correlations, the bulk spectral density deforms from the semicircle law via an explicit combinatorial "hub" mechanism, yet we verify the flatness and decay hypotheses of the matrix-Dyson-equation framework (MDE), with numerical evidence supporting Tracy-Widom edge universality for every fixed $\rho<1$ of the exponential decay correlations; the degenerate limit $\rho\to1^-$ reduces to a symmetrized Volterra operator, connecting to the singular-value cascade identified in a companion BBP analysis. For power-law correlations $dt\sim t^{-\gamma}$, we identify $\gamma_c=1/2$ as the critical point for divergence of the bulk fourth-moment, while $\gamma=1$ marks the breakdown of the flatness condition governing the MDE edge analysis. We prove the fourth-moment transition exactly and find numerically that the self-consistent edge varies smoothly across $\gamma=1$, with no evidence of a kink or discontinuity.

Can a boundary determine the direction of circulation in a collectively moving active fluid? We study chiral self-propelled particles with nematic bulk alignment, confined by walls whose orientational coupling varies continuously from nematic to polar. For an isolated particle at a wall, we derive the exact parameter condition under which a stable orientation is tangent to the wall. With predominantly nematic wall coupling, however, the many-body circulation changes sign at a chirality that is nearly independent of the wall symmetry. This sign change follows a pronounced decrease in nematic order and disappears when bulk alignment is removed. As the polar wall coupling becomes dominant, opposite-handed circulation is suppressed and same-handed polar locking emerges. Thus local orientation at a wall and the direction of macroscopic circulation are selected by distinct physical processes: the wall determines the possible local orientations, whereas collective order determines whether those orientations control the global flow.

Starting from the cyclic duality tensors introduced by Vernier, Miao, and Yamazaki (VMY), whose endpoint-traced matrix-product operators obey $\mathbb Z_N$ Tambara–Yamagami fusion and realize topological defect lines of the compactified-boson conformal field theory, we retain the virtual endpoint as an $N$-state dynamical degree of freedom and construct an exactly movable seam in the spin-$\tfrac12$ XXZ chain at $q=\mathrm e^{\mathrm i\pi M/N}$ with $\gcd(M,N)=1$. The local movement identity holds for any unitary $q$-Weyl pair; in the finite cyclic realization, all output phases are locally gauge equivalent and share the same four seam eigenvalues. On a ring, the output gauge becomes a directed twist on a single bond, while endpoint conjugacy reduces the $2N$ labels to two relative $\mathbb Z_2$ flux classes. An explicit antiunitary symmetry protects the class $\eta\equiv M-1\pmod 2$: for even $N$ it pairs distinct charge sectors isospectrally, whereas for odd $N$ it fixes one sector and squares to $-I$ there. Hence every many-body energy eigenspace in the protected class has even multiplicity. The source value $\eta_{\rm VMY}=1-M$ satisfies this condition for every coprime root, whereas the ungauged value $\eta=0$ does so only for odd $M$. Exact finite-size controls show that the opposite class can contain simple levels, so a global flux invisible to local gauge equivalence distinguishes the two classes spectrally.

Denoising score matching trains diffusion models by regressing onto a conditional score, although generation ultimately requires the marginal score. The two objectives share the same population minimizer, but the conditional target remains random at fixed noisy state and introduces an irreducible excess in the training loss. We isolate this excess and show that, for a general corruption kernel under mild regularity assumptions, it is exactly the trace of the Fisher–Rao metric of the conditional endpoint family, integrated along the diffusion trajectory. This gives an exact conditional-variance decomposition of the denoising objective and identifies the information geometry observed in diffusion latent spaces as an intrinsic component of the training loss. We derive the result from a Schr"odinger bridge variational principle, in which the ideal objective arises as excess path-space relative entropy. For corruption diffusions, the Fisher term is proportional to the rate at which the noisy state loses mutual information about the clean data, separating the loss floor into an information flow determined by the data and a weight determined by the corruption schedule and objective. In the Gaussian case, this yields a closed form for the floor, recovers reparametrization invariance of the continuous-time objective, and relates its high-SNR divergence to the information dimension of the data. Finally, we show that raw losses obtained with different noise ranges or weightings need not rank models consistently because they contain different additive floors, and contrast the second-order geometry seen by training with the third-order conditional statistics entering numerical sampling error.

Motivated by the ubiquity of ramified fractal deposits in nature and engineered systems, we investigate the irreversible adsorption of diffusion-limited aggregation (DLA) clusters on a square lattice. We study the role of cluster shape diversity on jamming properties of the system by systematically controlling the number of distinct shapes used across and within realizations, encompassing both monodisperse and polydisperse model variants. Our large-scale simulations over a broad range of cluster sizes $2\leqslant k\leqslant4096$ show that the jamming density decreases with cluster size as a power-law $p_j(k)-p_j^\infty\sim k^{-\alpha}$. Both $\alpha$ and $p_j^\infty$ are found to depend on the degree of shape diversity, with $\alpha$ ranging from $0.374(2)$ to $0.417(1)$. It is observed that increasing shape polydispersity promotes denser packing. Importantly, the fluctuations of the jamming density exhibit distinct scaling behavior: $\sigma(L)\sim1/L$ for a fixed pool of cluster shape(s), but remain $L$-independent when the pool of shape(s) is refreshed across different realizations. Furthermore, our results demonstrate that the differences between the model variants systematically diminish with increasing $k$ and are expected to vanish as $k\to\infty$ due to the statistical self-similarity of the DLA clusters.

Biological and artificial networks compute by transforming time-dependent inputs into functional outputs. Because the internal state of a stochastic network relaxes on finite timescales, its output generally lags behind a changing environment, producing computational errors. We show that for reversible continuous-time Markov networks the error admits a universal thermodynamic bound. Decomposing the total error into representation and lag contributions, we derive an inequality relating the lag error to the entropy production rate and a memory time equal to the integrated equilibrium autocorrelation of the output observable. The bound implies that accurate dynamical computation requires either substantial dissipation or long-lived memory encoded in slowly relaxing modes. We demonstrate these principles in artificial Markov networks and in models of biochemical information processing. Our results establish a thermodynamic limit on information processing in stochastic networks and provide a quantitative framework for understanding the energetic costs of biological computation.