Papers

Onsager solved the two-dimensional Ising model in zero field, but no solution is known in a magnetic field. We prove that in any dimension $d\ge2$, at every fixed dimensionless field outside a countable set, the free energy obeys no algebraic differential equation in the coupling, even locally. The obstruction arises from droplet geometry: the maximal droplet volume grows as the $d/(d-1)$ power of its boundary size, while an integer band in the pressure coefficients protects the extremal contributions against cancellation. Our result excludes Onsager-type solutions and closed forms in elliptic, hypergeometric, or Painlevé functions of the coupling at these fields.

Stochastic physical computers use random transitions between states to process inputs. We quantify their ability to solve distinct tasks as the control parameters of a device vary. For Markov jump devices, we bound the number of classification tasks attainable at a prescribed output margin, with each task defined as a binary labeling of fixed inputs. Combining geometric packing with fluctuation-response inequalities, we bound this number in terms of the control range and dimension, rate sensitivities, output fluctuations, and entropy production. For state and net-current observables, when controls change kinetics without changing thermodynamic forces and energies, the number of tasks is shaped by entropy production and output fluctuations. If the product of their maximum values over the allowed control settings and inputs is too small, the device can perform at most one task. An exactly solvable two-state switch illustrates how sufficient driving and observation time enable barrier tuning to select copying or inversion.

The resetting of stochastic processes has become a key mechanism appearing in many research fields, such as searching for a target, the transmission control protocol, biology, chemistry, finance, insurance, etc., with the main interest concerning the first passage time (FPT) by the process under resetting. In this paper, we focus on the exit time $\mathcal{T}_L$ from the interval $(-L, L)$ of Lévy flights (LF) under resetting, but we also consider spectrally negative Lévy processes (SNLP). As the main result, we find the asymptotics of the mean first passage time (MFPT) as $L$ tends to $+ \infty$. For LF with $\alpha \in (0, 2)$, the scaling behaves as $L^\alpha$ regardless of the reset rate and the asymmetry of the initial condition, a behaviour completely different from that for the known case of Brownian Motion ($\alpha=2$). For the symmetric $\alpha$-stable case with $\alpha \in (0, 2)$, we also found that taking $r \to \infty$ with fixed $L$ yields a finite MFPT, which therefore may be used as a valid approximation. For completely asymmetric stable processes, we show that the scaling is very different from that for LF, and point out a method to obtain the exact distribution of FPT under resetting. The analytical calculations are verified by numerical simulations of the processes under resetting.

We summarize previously published computer simulation studies of a metal electrodeposition model that considers diffusive cation flux, a fast reaction in contact with the electrode or with the growing deposit, and adsorbed atom diffusion in finite time windows. Simulations with various parameters show compact, fractal, dendritic deposits, and dynamic transitions between different morphologies during the growth of individual samples. The dendritic shapes are characterized by hierarchical organizations in which branches of a given order reproduce the shape and crystalline orientation of the branches of the previous order, in contrast to the random branching of the fractal deposits formed by DLA and related models. The simulations show dendrites with maple leaf shape in SC lattices, pine tree shape in FCC lattices, and flower-like shape in HCP lattices, with surfaces predominantly oriented in the lowest-energy configurations of each lattice. Simulations with nucleation restricted to a nanoscale seed show the initial formation of faceted particles followed by dendrite formation, in agreement with silver electrodeposition on substrates patterned with gold nanoparticles. A quantitative application to faceted and dendritic silver obtained in the same experiment provides values of the model parameters which are consistent with the characteristic widths of these structures being of the same order of magnitude of the diffusion lengths of atoms on (111) and (001) surfaces. Using an extended model for iron electrodeposition on Si(100), the simulations qualitatively reproduce the initial formation of multilayer islands, small oscillations of the roughness of a polycrystalline compact film after island coalescence, and instability development. Possible directions for applying this modeling to the electrodeposition of other materials are suggested.

AI-enabled computational drug discovery is advancing rapidly in predicting molecular structures, binding poses and affinities, but ligand dissociation kinetics remain harder to access. Bound-state residence time, important for biological response and kinetic selectivity, is not fixed by equilibrium affinity but depends on the dissociation free-energy landscape and dissipative friction effects. Here, we show that restrained umbrella-sampling trajectories can be used to calculate residence times on the minutes timescale. Time-resolved coordinate fluctuations yield friction profiles that incorporate non-Markovian effects on dissociation kinetics. Combining them with the free-energy profile, we predict a residence time of $\tau_{\rm res}$ = 275 s for the adenosine A$_{2A}$ receptor with ZM241385 (comparable to the experimental value of 125 s) and reproduce the experimental ranking of wild type and two receptor mutants. For HSP90 with compound 18 and RNase S with the S15 peptide, we predict $\tau_{\rm res}$ = 2,169 s and 2,259 s (experimental values are 833 s and 2,439 s). Neglecting memory effects on residence kinetics overestimates $\tau_{\rm res}$ by factors of 2.6 to 29.

Echo State Networks (ESNs) are fundamentally important from the conceptual perspective of AI, because they provide simple and tractable frameworks for understanding temporal information processing, memory, and learning in dynamical systems. They are composed by an interconnected reservoir whose connectivity matrix remains constant over time and only the output weights are updated during the training period. In particular, ESNs employing online training allow the incremental adaptation of the output weights as data is received, making them particularly suitable for applications in which new input data becomes available over time (non-stationary environments). A key objective in the study of such learning structures is to determine which statistical properties of the reservoir enhance computational efficiency and maximize prediction performance. To this end, we investigate the effects of reservoir topology on learning performance, considering weight matrices generated from Erdos-Renyi random networks and Watts & Strogatz small-world networks. As test data we use the Lorenz and Rossler models in the chaotic regime and the FitzHugh-Nagumo model in the limit cycle regime. In the case of random Erdos-Renyi reservoirs, our simulations show that best performances are obtained for sparse reservoirs and especially when the link-density is near and immediately above the critical point of mean-field bond percolation. Watts & Strogatz reservoirs are shown to demonstrate best performance also for small values of link-density, compatible with the mean-field bond percolation when taking into account the specific nonlocal ring structure of the Watts & Strogatz reservoirs. These studies on the influence of the reservoir architecture and hyperparameters on enhancing the accuracy of ESN predictions provide an efficient framework for real-time forecasting in dynamically evolving systems.

We investigate the statistical properties and ergodic behavior of the absolute area below the trajectory of a particle subject to stochastic resetting and moving according to a scaled Brownian motion with exponent $\beta$. We compare the contributions to the absolute area from the waiting times between resets and the backward recurrence time. Using the renewal formalism we derive the lower-order moments of the absolute area under both Poissonian and heavy-tailed power-law resetting waiting time distributions with exponent $\alpha$. For Poissonian resetting, stochastic interruption suppresses fluctuations, driving the area to be ergodic, regardless of the value of $\beta$. In contrast, power-law resetting yields a rich spectrum of ergodic regimes. For $0 < \alpha < 1$, the system displays weak ergodicity breaking and the maximum contribution dominates the area accumulated during the waiting times. For $1+\beta < \alpha < 2$, we unveil an ergodic transition exclusive to the subdiffusive regime at $\alpha=1+\beta$, where ergodicity is restored. These results clarify the subtle interplay between anomalous diffusion and power-law waiting times between resettings. Our results are tested by numerical simulations exhibiting an excellent agreement.

We study quantum van der Pol oscillator in which single-photon pumping competes with a nonlinear two-photon dissipative channel to produce a quantum limit cycle, and the question of how two such oscillators with non-identical intrinsic frequencies synchronize in the sense of phase locking when coupled dissipatively to one another. For a single oscillator, starting from a Lindblad description of the dynamics, we derive the exact Wigner-function evolution equation, and show that its Fokker–Planck approximation admits in the appropriate regime an equivalent classical Itô stochastic description that reproduces remarkably well the full Lindblad dynamics. Notably, the stochastic approach provides an efficient means of capturing system dynamics in the semiclassical regime, where a large number of energy eigenstates contribute and direct numerical simulations become computationally demanding. Restricting to the three lowest Fock states and using a parity symmetry, we obtain in closed form the stationary-state density matrix and its Wigner-function representation that displays pronounced nonclassical features. For two non-identical oscillators, we study the full Lindblad dynamics numerically and characterize synchronization through the stationary-state order parameter as a function of frequency mismatch and dissipative coupling. We find that increasing the effective nonlinear dissipative strength suppresses the synchronized region. Restricting the two oscillators to the three-level qutrit subspace, a parity symmetry reduces the stationary-state problem to an exact $41$-dimensional linear system, allowing to compute the synchronization order parameter. In this reduced description, results in the limit of large dissipation agree closely with those from the full dynamics, while exhibiting in the limit of small dissipation a double-peak synchronization structure accompanied by a phase reversal.

Fractional Brownian motion (fBM) is a model of anomalous diffusion parameterised by a Hurst exponent $H \in (0,1)$ and a generalised diffusion coefficient $D_H > 0$. We jointly estimate $H$ and $D_H$ using maximum likelihood (MLE) from density measurements with Poisson counting noise and single-particle trajectory with Gaussian localisation error. We show that one density measurement in time cannot infer both $H$ and $D_H$ and that several time points are needed, which matters most for inference precision. For trajectories, we show that a neural network trained with a squared error loss approximates the posterior mean of $H$, which can be computed exactly at negligible cost. Paired with the profile-likelihood estimate of $D_H$, the posterior mean has the lowest root mean squared error in both $H$ and $D_H$, except near $H=0$ and $H=1$ where MLE estimates $H$ better. In vesicle trajectories from two cell types, $H$ and $D_H$ form a continuum rather than distinct modes of motion. The posterior probability that each window within a track is subdiffusive or superdiffusive shows that $26\%$ of MRC5 fibroblast and $21\%$ of HeLa vesicle trajectories contain both subdiffusive and superdiffusive windows, against $2\%$ and $7\%$ expected from estimation uncertainty alone. Intracellular cargoes therefore switch between subdiffusion and superdiffusion over time rather than forming populations with fixed $H$.

In the Mpemba effect, a system prepared farther from equilibrium relaxes faster than one prepared closer to it. Its persistence across diverse systems, and under different dynamics of the same system, suggests that it is largely rooted in equilibrium properties, with the dynamics deciding only which mode relaxes slowest. Here we propose a simple rule of thumb for anticipating the Mpemba effect: the effect is expected when a single low-order equilibrium moment is nonmonotonic in temperature. The bath singles out this moment as the slowest to relax, so that its displacement from its bath value sets the amplitude of the slowest relaxation mode. We establish this relation exactly for low-dimensional Ornstein–Uhlenbeck processes. We then extend the rule to mean-field models by approximating their relaxation near the final equilibrium state by an Ornstein–Uhlenbeck process. For the mean-field Ising antiferromagnet, which we solve exactly in the thermodynamic limit, this approximation reproduces the main structure of the Mpemba phase diagram, including strong effects far from any phase transition. Finally, we give a general prescription for mean-field systems: identify the slowest symmetry-allowed moment of the normal coordinates at the bath, and follow its equilibrium value as a function of preparation temperature. This offers a practical route from equilibrium observables to anomalous relaxation without diagonalizing the dynamics.

Aging and relaxation of glasses proceed through localized rearrangements that also generate long-ranged mechanical responses in their surroundings. We develop a theory that treats these rearrangements as internal microseismic sources, and thereby separates the direct effects emerging from an event from the effects from the far-field displacements it generates. These far-field disturbances propagate and relax through the viscoelastic medium through which they move, producing a stochastic background of weak but numerous perturbations at any given location. Combining the description of local events from the Random First Order Transition theory with this propagating background, we derive a unified equation for the dynamical structure factor of a relaxing glass. The theory identifies a finite wave-vector and time window in which the growing viscoelastic far-field disturbances can produce compressed exponential relaxation, which has been observed using X-ray photon correlation spectroscopy. At higher wave vectors that resolve local jumps, heterogeneity of the local event dynamics instead produces stretched exponential relaxation. The crossover between these behaviors depends on the event statistics and the scattering phase accumulated across the region reached through viscoelastic propagation from the numerous distant sources.

Mandlebrot's coastline paradox reframes measurement as a joint property of an object and its ruler. Here we ask how observational resolution shapes the apparent structure of neural computation. We introduce a scale-indexed decomposition that separates the predictive information captured by direct dependencies from the residual outside that model family. Exact constructions show that projection can convert higher-order dependence into pairwise structure. Projection can increase the direct fraction of surviving information even as total predictive information decreases. A schematic branch-to-soma cascade grounds these effects in local coincidence detection, saturating integration and somatic mixing. Resolving organized nonlinear subunits improves approximation and raises effective representational rank. In a nested hierarchy, these gains occur without increasing information about the target. This distinction separates information availability from access by a restricted readout. A point-neuron or direct population model therefore establishes an effective description at a specified scale. It does not uniquely identify the finer computation that generated the observed relation. Which resolution is adequate depends on the observable and perturbation of interest.

The mutual information of measurement of a local operator between two spatial regions characterizes the reduction in the uncertainty of measurement outcomes in one region given the outcome in the other. We study the Rényi-Shannon mutual information of measurement in conformal field theories (CFTs). Explicit calculations for scalar primaries and descendants in large $N$ CFTs are performed in the two extreme limits of the intervals being adjacent or largely separated. The results depend on only the cross ratio and the scaling dimension $\Delta$ of the operator being measured, with striking similarities to the mutual information of entanglement. We find a surprising quadratic dependence as $(\Delta-1/2)^2$ for adjacent intervals. This dependence superficially seems to violate the information processing inequality, which we discuss and resolve. We also offer a holographic interpretation of the mutual information of measurement.

Generators of continuous-time quantum Markovian evolution, known as Lindblad operators, play a key role in the theory of open quantum systems. The question of how to define and characterize random Lindblad operators has attracted considerable attention in recent years. Purely dissipative random Lindbladians have been extensively studied using toolboxes of free probability and non-Hermitian random matrix theories, which helped, among other results, to uncover a characteristic lemon-like spectral support. In this work, we focus on random Lindbladians with a Hamiltonian component. We analyze three ensembles of increasing complexity, designed to illustrate the joint effects of dissipative and Hamiltonian dynamics. While the first two ensembles allow for an exact analytic treatment with standard probabilistic and free-probability methods, the generic case of independently random Hamiltonian and dissipative components requires a novel framework that combines operator-valued free probability with sequential noise averaging. For this ensemble, our approach preserves the underlying tensor-product structure of the Lindblad operator and derives a general equation for the spectral boundary. We characterize the effect of Hamiltonian-induced spectral squeezing and explain how the spectral support changes with the relative Hamiltonian strength and the rank of the dissipative component.

We apply large $N$ expansion techniques to derive kinetic equations for strongly coupled, far-from-equilibrium field theories with $O(N)$ symmetry. For large $N$ vector models, the quasi-classical approximation holds. Incorporating arbitrary momentum-dependent interactions, we show the dynamics obey the standard kinetic equation, with the scattering amplitude given by the retarded propagator of the auxiliary Hubbard-Stratonovich field. This has broad applications to systems like spin wave and Langmuir ion-acoustic turbulence. For large $N$ random coupling (SYK-like) models in $d$ dimensions, leading-order melon diagrams induce order-one propagator renormalization and finite spectral width. The corresponding kinetic equation, unlike those for standard weakly interacting systems, does not have a local-in-time collision integral. We find evidence for a stationary, scale-invariant infrared solution, revealing a potentially novel strong turbulence scaling exponent.

Interactions turn a gas into a fluid. We show that two-body loss can take their place. Correlated loss induces elastic scattering, as required by the optical theorem, which dominates at strong loss via the quantum Zeno effect. A nondegenerate gas with only two-body loss thus flows hydrodynamically, with viscosity and thermal conductivity close to those of the unitary Fermi gas. As loss heats the gas, both grow in time with a universal exponent 3/8. Unlike single-particle loss, two-body loss can engineer collisions, and hence transport, in quantum matter.

Under local Lindbladian evolution, the growth of conditional mutual information and its associated Markov length scale is not limited by Lieb-Robinson bounds, yet it has been unclear how quickly the Markov length can increase. We show that an arbitrarily short, strictly local Lindbladian can generate infinite Markov length from a product state. We also construct strictly local Lindbladians that converge rapidly to steady states with algebraically decaying conditional mutual information. Despite their long-range conditional correlations, the states we construct are local reversibly connected to a product state by sublinear depth circuits. Thus infinite Markov length does not imply slow relaxation nor obstruct phase stability when suitably defined.

Non-Abelian anyon chains whose interactions favor a single fusion channel host quantum critical ground states described by minimal-model conformal field theories (CFTs) protected by a topological symmetry. We show that their measurement-only counterpart, where non-commuting fusion charge measurements act locally on the anyons of a chain of $L$ sites, provides a fundamental example of a non-unitary CFT controlling a non-Abelian learning problem. Mapping the monitored dynamics to a random tensor network, we numerically find $1/L$ scaling Lyapunov gaps, logarithmic entanglement scaling with the chord length, and an effective central charge in the Shannon entropy of the measurement record. The conserved topological charge sharpens with dynamical exponent $z= 1$ and is learnable by a decoder on an $O(L)$ time scale. As the topological symmetry is a non-invertible symmetry of the $SU(2)_k$ anyon theories, we establish the monitored golden chain $(k=3)$ as a non-Abelian generalization of the weakly (Kramers-Wannier) self-dual quantum critical point of the toric code $(k=2)$, and the first of a family for $k\geq 3$.

Quantum simulators with disordered spin Hamiltonians offer a natural route to Haar-like unitary ensembles, but face a competition. Disorder enhances randomness, yet strong disorder suppresses dynamics and localizes the system in the computational basis. This suggests an optimal intermediate disorder strength for approximating a unitary $k$-design, which has so far been identified mainly empirically. Here, we develop a perturbative theory for the moment gap $\Delta^{(k)}$, the deviation of the $k$-th moment operator from its Haar value, for the full spectrum of the interacting XXZ chain in a fixed-magnetization sector. We find the non-monotonic asymptotic scalings $\ln \Delta^{(k)}\sim -\sigma^2$ at weak disorder and $\ln \Delta^{(k)}\sim -1/\sigma$ at strong disorder, whose crossover sets an optimal disorder strength $\sigma_c\sim J_{xy}$, where $J_{xy}$ is the energy scale of the non-random interaction. We further show that a multi-quench protocol further suppresses the gap exponentially in the number of quenches. Numerical simulations confirm both scalings and this exponential suppression, and we demonstrate the usefulness of the protocol for classical shadow tomography. This work suggests that strong disorder may block both thermalization and the formation of unitary designs through a common localization mechanism.

Stochastic resetting with stochastic return (SR) has recently emerged as an effective and practically relevant strategy for controlling first-passage phenomena and optimizing search processes by significantly reducing completion times in a wide class of stochastic systems. While most theoretical studies assume instantaneous return (IR), in realistic systems the return to the resetting position typically occurs over a finite time. We consider a 1-d diffusing particle in a harmonic trap with stiffnesses $k_1$ and $k_2$ during search and return, respectively. The particle searches for the target and, upon resetting at rate $r$, enters the return phase, continuing until it reaches either the origin or the absorbing target at $L>0$. Notably, the model permits target detection throughout the return phase, distinguishing it from IR scenarios. We analytically derive the MFPT for our model and determine parameter regions where SR enhances or suppresses search efficiency over the underlying dynamics, constructing the corresponding phase diagram using the coefficient of variation criterion. We further identify regimes in which SR is more efficient than IR using the SR criterion. This behavior is tested across different parameter sets taken from experimental studies by Goerlich et al., Biroli et al., and Besga et al. We map the parameter values reported in existing experimental studies onto our theoretical phase diagram, thereby identifying the regimes in which SR outperforms IR. In particular, we find that the most relevant region of the phase space, where SR is most beneficial corresponds to larger values of the potential strength in the search phase and lower values of potential in the return phase. Our results provide experimentally testable predictions and bridge the gap between theoretical resetting models and optical trap mediated finite-time return dynamics.

We study the long-time, large-distance asymptotics of finite-temperature dynamical Fredholm determinants using effective form factors. The method expresses these asymptotics as a functional of an effective phase shift. We determine its two branches on either side of a quadratic stationary point and the transition profile joining them. The profile is expressed through parabolic-cylinder functions. Its connection to the high-temperature Gaussian $\beta$ ensemble fixes the finite normalization, in agreement with an independent Riemann–Hilbert analysis. We also show that the leading exponential asymptotics suffice to recover the Euler-scale prediction of generalized hydrodynamics for the dynamical structure factor of hard rods.

Gauge-equivariant graph neural networks generate ordered products of gauge links through local message passing, but the geometry of these internal structures is not captured by the receptive field alone. We investigate the statistical ensemble of closed lattice walks generated by recursive node- and edge-feature operations, independently of network training. Analytical and numerical results reveal a separation between rapid growth of contour length and much slower spatial expansion: deeper compositions generate increasingly long paths through repeated traversal of relatively compact regions. Loop expansions of fermionic observables provide a physical interpretation of this hierarchy, showing how spatial locality remains compatible with high-order dependence on nearby gauge fields. These findings identify complementary roles of network depth in extending spatial reach and enriching the representations constructed within that reach, providing a geometrical perspective on learning lattice gauge observables.

Rare events, such as crystal nucleation in mildly supercooled liquids, are characterized by waiting times that can be much longer than the timescale of the underlying microscopic dynamics. The mean first-passage time (MFPT) formalism [J. Wedekind and D. Reguera, J. Phys. Chem. B 112, 11060 (2008)] provides a route to reconstruct one-dimensional free-energy profiles from the MFPT and steady-state distribution measured along a reaction coordinate, but conventional implementations become inefficient for sufficiently high barriers because spontaneous crossings are rarely observed. We introduce a "top-start" extension that initiates trajectories near the barrier top and reconstructs the free-energy profile from their subsequent evolution away from the barrier toward lower-free-energy regions. We establish the equivalence between the top-start and two-region constructions using a Markov-chain transition-matrix formulation. We validate the method using one-dimensional random-walk simulations across low, medium, and high free-energy barriers, with transition-matrix calculations providing an exact benchmark for the corresponding discretized models. The top-start reconstruction remains accurate in the high-barrier regime where conventional MFPT sampling becomes prohibitively inefficient.

The symmetric exclusion process (SEP) is a paradigmatic model of interacting particle transport. Its current–density correlations are governed by an infinite many-body hierarchy of equations. Only recently, this hierarchy was found to collapse at large scales onto a single closed equation. Is this remarkable simplification created by coarse graining, or does it reflect a deeper property already present in the microscopic dynamics? Here we show that the second scenario is realized. At arbitrary time on the lattice, the entire hierarchy collapses onto a single linear equation which is exactly equivalent to a persistence problem for a single auxiliary random walker. Thus an interacting many-body problem reduces exactly to a genuine one-body problem before any scaling limit is taken. This reduction determines the complete finite-time correlation profile, including during nonequilibrium relaxation. More broadly, the microscopic operator uncovered here opens a route to more general correlation functions in the SEP, and may point to a general organizing principle for nonequilibrium interacting particle systems.

Multiplayer social dilemmas on hypergraphs show a variety of emergent phenomena, which has been attributed to group interactions. Here we test whether pairwise dynamics can reproduce them as well. We derive the mesoscopic Langevin equation of a testbed model and find the operator content of absorbing phase transitions: a directed-percolation line, a tricritical point, and a first-order region whose spinodal is the explosive transition. In our analysis, three-player games only set the values of the Landau coefficients. We construct a strictly pairwise model with short-lived memory, in which every event involves at most two entities, that reproduces these coefficients term by term and has exactly the same mean-field fixed points. Simulations confirm that the two dynamics share mean-field critical and tricritical scaling and the size of the critical mass, and that a purely three-player game on a two-dimensional triangular lattice lies in the directed-percolation class. For these games, the explosive transition and the critical mass therefore do not require group interactions, and the critical behavior is that of the pairwise theory.

We develop a macroscopic fluctuation theory for diffusive classical lattice gases subject to continuous coarse-grained monitoring. Treating measurements in the typical-outcome (quenched) regime, we show that observation adds a quadratic confining term to the MFT action that pins the density to its hydrodynamic profile. We derive sufficient conditions under which, in the presence of monitoring, the current large-deviation function remains convex, the additivity principle holds, and dynamical phase transitions are excluded. For particle-hole-symmetric one-dimensional models we find that monitoring suppresses dynamical phase transitions and can change their order from second to first, as we demonstrate in the Katz–Lebowitz–Spohn model. In the strong-measurement limit, we find that the current distribution becomes Gaussian and determine the scaling of its cumulants: they follow simple power laws when the mobility remains nonzero throughout the system, but exhibit anomalous logarithmic scaling when the mobility vanishes at the boundaries.

We examine how the Curie–Weiss cell fluid model can be quantitatively related to real fluids by determining its microscopic parameters from experimental critical-point data for water, carbon dioxide, and three polyol ester lubricants (POE5, POE7, and POE9). The microscopic parameters of the model are determined from the experimental values of the critical temperature and critical density: the global attraction coupling constant is fixed by the critical temperature, and the cell volume by the critical density. The critical pressure then follows as an independent model prediction, deviating from experimental values by 10–41$\%$ across the studied substances. Varying the ratio of local repulsion to global attraction $f=J_2/J_1$ over a wide range has only a weak effect on this deviation. For $f\geq1$, the model's critical compressibility factor lays within a narrow range $Z_c\approx0.382-0.386$, remaining close to the mean-field van der Waals value $Z_c=3/8=0.375$ and consistently overestimating experimental values. The best agreement with experiment is obtained for the polyol ester lubricants and improves along the POE5–POE7–POE9 series with increasing molar mass, suggesting that multiple-occupancy cell fluid models are well suited to systems of large molecules, particularly soft-matter systems with bounded interaction potentials. We further show that generalizing the model by introducing a temperature- and phase-dependent effective attraction allows it to describe a triple point and to reproduce the broad range of critical-to-triple temperature ratios $T_c/T_{\mathrm{tr}}$ characteristic of real fluids.

We demonstrate that the symmetry of magnetoelastic coupling governs the topological organization of composite defects and can qualitatively alter phase-ordering kinetics. In a two-dimensional theory of an in-plane magnetic vector coupled to elastic strain, we find that integer magnetic vortices bind pairs of elementary elastic half-defects. Isotropic magnetostriction produces a core-induced elastic winding independent of the magnetic charge, giving defect binding without charge locking and leaving the magnetic sector with essentially XY-like coarsening. In contrast, quadrupolar magnetoelastic coupling locks magnetic and elastic defect charges: continuous rotational symmetry favors $q_\phi=q_\theta$, whereas crystalline anisotropy can reverse the locking to $q_\phi=-q_\theta$. We reveal that both locking sectors display anomalously slow vortex annihilation: defect density shows a power-law decay $t^{-2/5}$, while the average defect-velocity scales as $t^{-4/5}$. These results are consistent with a dynamic exponent $z\simeq 5$. We show that this coarsening slowdown is associated with large anisotropic elastic friction. An adiabatic elimination of the elastic field reveals that isotropic magnetostriction merely renormalizes local magnetic interactions, whereas orientational coupling induces effective nonlocal interactions between magnetic spins. Our experimentally testable results thus establish magnetoelastic coupling symmetry as a means of controlling defect topology and ordering kinetics.

We test the effective-gravity prediction of global thermodynamics using standard molecular dynamics of a two-dimensional Lennard-Jones fluid. Under weak heat conduction with the lower boundary hotter than the upper boundary, the transition between liquid below gas and liquid above gas shifts from zero to finite downward gravity. Using independently measured equilibrium saturation pressures, we calculate the shift predicted by global thermodynamics and find agreement with the observed transition shift. The transition occurs at zero effective gravity, where the hydrostatic pressure difference balances the saturation-pressure difference between the two boundaries. The hysteresis response under heat conduction also agrees with the equilibrium response when plotted against effective gravity. These results establish the predictive power of global thermodynamics for nonequilibrium structure formation.

This work is a step towards a general understanding of fluctuations for systems of particles described at large scale by fractional diffusion. First, we derive formally a Large Deviation Principle for the empirical measure of mean-field interacting particles with a Lévy-type noise. In the case of independent particles, this unveils a generalized gradient flow structure at large scales. Second, we derive and solve numerically a stochastic Partial Differential Equation describing the fluctuating hydrodynamics of this system. The results compare well with direct numerical integration of the particles' dynamics.