Differentiable physical networks provide a simple setting in which learning can be studied through the interaction between trainable parameters and physical equilibrium constraints. We investigate sequential learning in differentiable resistor networks governed by Kirchhoff's laws. Although individual input–output mappings can be learned by gradient-based adjustment of edge conductances, sequential training on conflicting tasks produces catastrophic forgetting. We show that forgetting is controlled by task conflict and by the degree of adaptation to the new task. Uniform anchoring and normalized gradient-weighted anchoring reduce forgetting only by increasing the final loss on the new task, giving a clear forgetting–adaptation trade-off. We also show that forgetting is associated with localized conductance changes on high-current edges, giving a physical interpretation as reconfiguration of dominant transport pathways. Broader random-task ensembles show that the strongest forgetting occurs when the second task reverses the output ordering imposed by the first task. Finally, comparisons across Erdős–Rényi, small-world, scale-free, and random-geometric graph ensembles show that topology changes the forgetting–adaptation balance. These results position differentiable resistor networks as compact, physically interpretable test beds for studying continual learning in tunable matter.

We develop a physics-based analytical model for the ferroelectric-to-paraelectric phase transition in poly(vinylidene difluoride-co-trifluoroethylene) [P(VDF-TrFE)] copolymers. The low-temperature ferroelectric phase is an orthorhombic crystal analogous to the poly(vinylidene difluoride) β-phase, while the high-temperature paraelectric phase is a conformationally disordered (condis) crystal. The model for a single crystal consists of two coupled components. The first is an Ising-type model that calculates crystal polarization as a function of temperature and electric field by treating a polymer chain as a sequence of coupled dipoles in a molecular field, self-consistently induced by other chains. The key model parameter, the energy of a gauche dihedral, is a strong function of the transverse lattice parameter (the interchain spacing). The second component determines the optimal lattice parameter by minimizing the crystal free energy, which balances interchain potential energy against chain conformational entropy. All single-crystal parameters are calibrated against molecular dynamics simulations of a quasi-infinite P(VDF-TrFE) crystal. To model real semicrystalline polymers, the single-crystal model is extended by introducing a Gaussian distribution of phase transition temperatures $T_c$ across crystallites. The distribution parameters are calibrated against literature experimental data for the remanent polarization of P(VDF-TrFE). This extended model calculates hysteresis loops and predicts their strong temperature dependence. At $T<T_c$, the model predicts a wide hysteresis loop with a large coercive field, characteristic of a normal ferroelectric. Near $T_c$, the loop becomes narrow, exhibiting the slim hysteresis specific to ferroelectric relaxors. The calculated hysteresis loops and the associated temperature-dependent dielectric permittivity are in semiquantitative agreement with literature experimental data.

The ferromagnetic spin-2 quantum Blume-Capel model in the presence of a transverse crystal field interaction is studied by employing a variational approach based on Bogoliubov inequality for the free energy and an exact mapping of the ground state. The thermodynamic properties have been obtained using a single spin cluster, which is equivalent to the usual mean-field approximation. The temperature dependence of the magnetization has been analyzed and the global phase diagram, as function of the model parameters, has been obtained for any values of the coordination number of the lattice. A variety of quantum phase transitions, multiple and multicritical points, are present in several topologies of the corresponding phase diagrams. The ground state properties of the system have also been obtained through an exact mapping of the spin-2 model onto another equivalent spin-1 Blume-Capel model in a transverse field. This mapping allows one to determine an exact asymptote formula of the phase diagram at zero temperature in the limit of large longitudinal crystal field for any lattice dimension.

The partition function and the spontaneous magnetization of a two-dimensional (2D) Ising model with the next nearest interactions at zero magnetic field are derived analytically. At first, the transfer matrices are analyzed in three representations, i.e., Clifford algebraic representation, transfer tensor representation, and schematic representation, to inspect nontrivial topological structures in this system. The system is equivalent to a triangular Ising model plus an interaction along the $z$ axis, so that the approaches developed for the 3D Ising models are modified to be appropriable for analytically solving the solution of the 2D Ising model with the next nearest interactions. The comparison with the exact solutions of other Ising lattices reveals that either the increase of the number of interactions in a unit cell or the presence/increase of topological contributions enhances the critical point of the Ising lattices. The results obtained in this work are helpful for understanding the physical properties of the 2D magnetic materials.

We show how the trajectories of $d$-dimensional cellular automata (CA) can be used to systematically construct the ground states of $(d+1)$-dimensional classical spin models, and we characterize their quantum phase transition, when in the presence of a transverse magnetic field. For each of the 256 one-dimensional elementary CA we explicitly construct the simplest local two-dimensional classical spin model associated to the given CA, and we also describe this method for $d>1$ through selected examples. We illustrate our general observations with detailed studies of: (i) the $d=1$ CA Rule 150 and its $d=2$ four-body plaquette spin model, (ii) the $d=2$ CA whose associated model is the $d=3$ square-pyramid plaquette model, and (iii) two counterpropagating $d=1$ Rule 60 CA that correspond to the two-dimensional Baxter-Wu spin model. For the quantum spin models, we show that the connection to CAs implies a sensitivity on the approach to the thermodynamic limit via finite-size scaling for their quantum phase transitions.

In this article we present a comprehensive study of the totally asymmetric simple exclusion process with pausing particles (pTASEP), a model initially introduced to describe RNAP dynamics during transcription. We extend previous mean-field approaches and demonstrate that the pTASEP is equivalent to the exclusion process with dynamical defects (ddTASEP), thus broadening the scope of our investigation to a larger class of problems related to transcription and translation. We extend the mean-field theory to the open boundary case, revealing the system's phase diagram and critical values of entry and exit rates. However, we identify a significant discrepancy between theory and simulations in a region of the parameter space, indicating severe finite-size effects. To address this, we develop a single-cluster approximation that captures the relationship between current and lattice size, providing a more accurate representation of the system's dynamics. Finally, we extend our approach to open boundary conditions, demonstrating its applicability in different scenarios. Our findings underscore the importance of considering finite-size effects, often overlooked in the literature, when modeling biological processes such as transcription and translation.

While the behavior of virtual cathodes (VCs) in a space-charge limited gap in the absence of a magnetic field is well understood, it is less characterized for crossed-field gaps with perpendicular magnetic and electric fields. Thus, this study examines VC formation at steady state in a crossed-field gap with magnetic field $B$ below the Hull cutoff magnetic field $B_H$ for magnetic insulation. VC formation at the critical current density $J_c$ depends strongly on the initial electron velocity $u_0$ and $b=B/B_H$. For $u_0\le 2\mathrm{\Omega }D/\pi$, where $\mathrm{\Omega }$ is the cyclotron frequency and $D$ is the gap distance, there exists a threshold $b_{\mathrm{VC}}=B_{\mathrm{VC}}/B_H$ such that a VC forms between the cathode and anode at $J_c$ for $b<b_{\mathrm{VC}}$, but does not form for $b>b_{\mathrm{VC}}$. This is unlike the nonmagnetic case, for which a VC forms at $J_c$ whenever $u_0\ne 0$. When no VC forms in a crossed-field gap, the electrons accelerate upon emission from the cathode and decelerate near the anode, causing a peak in electron density. Thus, the limiting current no longer corresponds to the buildup of space-charge at or near the cathode, but instead to buildup at the anode. We also show VC formation for steady-state current densities $J<J_c$. While a VC also forms at steady state for $J<J_c$ in nonmagnetic diodes with $u_0\ne 0$, VC formation is still necessary at $J=J_c$. However, for crossed-field gaps, VC formation alone is neither sufficient nor necessary for the limiting current condition.

The cyclotron resonance dynamics of ions in a uniform magnetic field under the action of a plane left-handed polarized wave is considered. The dynamics of initially slow ions is nonlinear: they periodically synchronously (regardless of the initial phase of interaction) gain and then lose energy. The maximum acquired energy and the duration of such cycles depend, in particular, on the magnitude of the shift of the magnetic field in the interaction region relative to the resonant value (determined by the frequency of the wave) and the longitudinal wave number of the wave. The latter, in the case where the wave is an eigenmode, also depends on the magnitude of the shift. The possibility of optimizing the ion-cyclotron heating unit of VASIMR-type thrusters lies in determining the parameters of its magnetic configuration, at which the increase in the energy of ions during their flight through the resonant interaction zone is maximum. It is shown that the optimal value of the magnetic field in the interaction zone is approximately 0.5% higher than the resonant one, and a compact expression is obtained for the optimal length of the zone with a given field value.

Phase separation into compositionally and physically distinct domains is ubiquitous in (non)living matter ranging from alloys and emulsions to biomolecular condensates in cells. The organization of these domains can be controlled, for example, by nonequilibrium chemical reactions, external fields, or mechanical stresses. In this context, stationary states can emerge from effective long-range interactions resembling the electrostatics of charges. Here, I develop a theory predicting that externally controlled dynamic states, such as condensate motion, lead to an effective polarization and dipolar force fields even for microscopically nonpolarizable matter. The dipole-dipole interactions resulting from this translation-induced polarization cause directed coalescence of domains. This coarsening mechanism complements Ostwald ripening and coalescence due to Brownian motion or Marangoni flows, and has implications for controlling domains by electric fields or concentration gradients. Interestingly, the chemical potential gradients around a domain that nucleates material are exactly opposite to the hydrodynamic pressure gradients around an impermeable colloid that pushes the fluid, suggesting a competition between phase separation and hydrodynamics. In addition to chemical control, the motion of domains can also be driven by mechanical stresses. An example is the cell interior, where mechanical stresses are actively generated by molecular motors and opposed by passive viscoelastic stresses in the cytoplasm and nucleoplasm. Taking into account such active fluctuations in the theory predicts that the resulting fluid flows lead to Brownian motion with a suppressed or enhanced size scaling that modifies collision-coalescence. For active stresses with a long correlation time, the domains show superdiffusion on intermediate timescales. Together, these findings shed new light on the dynamics of domains in viscoelastic media and conserved order parameters in general.

Even at very low concentrations, the rheology of dispersions of charged semiflexible nanofibers differs from the rheology of the pure liquid, given the fiber charge, morphology, and interactions. At the nanoscale, the thermal motion of fibers is driven by the collective motion of the solvent molecules, but to what extent does the fiber presence and motion affect the self-diffusion of the liquid molecules? By studying the self-diffusion of water in dilute nanofiber dispersions using experiments and simulations, we can show that the interplay of fiber charge and motion on water mobility is more significant than the effect of the excluded volume caused by the charged particles.

We examined the Brownian motion of point defects in a two-dimensional hexagonal colloidal crystal, going beyond the conventional treatment that assumes constant diffusion coefficients. By extracting the spatially varying drift vector and diffusion matrix directly from experimental trajectories, we uncovered richer behavior than predicted by the simple diffusive limit. Within a general stochastic-dynamics framework, these measurements revealed an effective stochastic potential landscape shaped by the crystal's periodic structure. The energy differences between its local minima were consistent, to within an order of magnitude, with previous experimental estimates. Simulations of stochastic trajectories on this reconstructed landscape reproduced the essential features of the observed defect motion. This study illustrates how combining time-series extraction with theoretical analysis can expose effective energy landscapes and provide a powerful route to understanding complex dynamics in colloidal systems.

This work reports two independent experimental estimations of the dynamic strength of the body-centered tetragonal (bct) $\gamma$ phase of tin, which occurs at pressures above about 9 GPa and transforms promptly back to the ambient $\beta$ phase upon pressure release. Measuring strength in such a transient high-pressure phase is challenging. One measurement used free-surface Richtmyer-Meshkov instabilities generated with gas gun impact. Another set of measurements used ramp-release loading in a pulsed-power facility. Strength estimations came from comparison to simulations using a comprehensive multiphase modeling framework that includes equation of state, shear moduli, and strength separately for each phase, and treats mixed-phase regions. Both experimental methods found the $\gamma$-phase strength to be very low, within experimental uncertainty of zero. The existing literature on other materials, by contrast, almost universally reports higher strength in transient high-pressure phases compared with ambient phases. Recent Molecular-Dynamics simulations on tin in the literature showed almost zero deviatoric strength during a deformation-induced bct $\to$ bct transformation in which one of the $\gamma$-phase $a$ axes “flips” to the $c$ axis. This reorientation currently provides the most plausible explanation for the low observed strength in $\gamma$-phase tin.

This study investigates the first-passage-time (FPT) properties of particles with a broad class of positive stochastic diffusion coefficients (DCs), representing diffusion in heterogeneous environments or of particles with conformational fluctuations. We demonstrate that for diffusion in a one-dimensional semi-infinite domain with an absorbing boundary, particles will eventually reach the absorbing boundary with probability one. We also show that a stochastic DC provides higher transport efficiency in an early arrival of particles at the boundary than would be expected under diffusion whose DC is the ensemble average of the stochastic DC. Furthermore, a stochastic DC with a larger supremum exhibits a more efficient transport even if ensemble averages are the same. For ergodic DCs, we show three more properties: The mean FPT diverges, the enhancement of early-arrival efficiency diminishes over long times, and the FPT distribution converges to a Lévy-Smirnov distribution in the long-time limit. These properties are shown to arise from the convergence of the time-averaged DC to the ensemble average, with the convergence speed determined by the DC's fluctuation timescale. We finally discuss the similarities and differences of FPT properties between three-dimensional diffusion outside a spherical absorbing boundary and the one-dimensional diffusion. Our results indicate that fluctuations in DCs may need to be non-Markov and/or nonergodic to allow efficient transport of particles to distant targets. Our results also suggest that fluctuations in a DC play an important role, for example, in diffusion-limited reactions triggered by single molecules in physics, chemistry, or biology.

We investigate nonequilibrium phase coexistence associated with a first-order phase transition by numerically studying a one-dimensional Hamiltonian-Potts model with fractional spatial derivatives. The fractional derivative is introduced so as to reproduce the low-wave-number density of states of the standard two-dimensional model, allowing phase coexistence to occur in a minimal one-dimensional setting under steady heat conduction. By imposing a constant heat flux through boundary heat baths, we observe the stable coexistence of ordered and disordered phases separated by a stationary interface. We find that the temperature at the interface systematically deviates from the equilibrium transition temperature, demonstrating a clear violation of the local equilibrium description. This deviation indicates that equilibrium metastable states can be stabilized and controlled by a steady heat current. Furthermore, the interface temperature obtained in our simulations is in quantitative agreement with the prediction of global thermodynamics for nonequilibrium steady states. These results confirm that the breakdown of local equilibrium and the stabilization of metastable states are intrinsic features of nonequilibrium first-order phase transitions, independent of spatial dimensionality. Our study thus provides a minimal and controlled numerical model for exploring the fundamental limits of thermodynamic descriptions in nonequilibrium steady states.

The instability mechanism in general reaction-diffusion-advection systems is key to understanding flow-driven self-organization. Here we report the general conditions for instability in $d$-dimensional space, formally termed relative advection instability (RAI) given its exclusive dependence on the relative velocity difference. We demonstrate that the critical wave vector at the onset of instability aligns with the relative advection direction, leading to emergent traveling waves, whereas stationary periodic patterns only occur under specific orientations. Unlike the classical Turing paradigm, RAI is governed by a critical advection disparity rather than a diffusion ratio, allowing for patterns even with equal diffusion coefficients. Numerical simulations confirm that these patterns consist of traveling waves with distinct wavelengths, speeds, and amplitudes.

Detecting Lévy flights of cells has been a challenging problem in experiments. The challenge lies in accessing data in spatiotemporal scales across orders of magnitude, which is necessary for reliably extracting a power-law scaling. Differential dynamic microscopy has been shown to be a powerful method that allows one to acquire statistics of cell motion across scales, which is a potentially versatile method for detecting Lévy walks in biological systems. In this article, we extend the differential dynamic microscopy method to self-propelled Lévy particles, whose run-time distribution has an algebraic tail. We validate our protocol using synthetic imaging data and show that a reliable detection of active Lévy particles requires accessing length scales of an order of magnitude larger than its persistence length, if the variability in particle speed is moderate. Applying the protocol to experimental data of E. coli and E. gracilis, we find that E. coli does not exhibit a signature of Lévy walks, while E. gracilis is better described as active Lévy particles.

We demonstrate the onset of Rayleigh-Bénard convection (RBC) near the fuel-ablator interface of inertial confinement fusion (ICF) implosion simulations for the scenario in which Rayleigh-Taylor or Richtmyer-Meshkov instabilities are suppressed. This convective heating within the cold fuel can degrade the adiabat and therefore performance of ICF implosions even without mixing of fuel and ablator. Our work suggests additional considerations to realize design adiabats in otherwise ideal ICF implosions: first, via control of the temperature differences between ablator and fuel and, second, control of the fuel acceleration which we show has a complex interplay with the RBC dynamics.

Proper management of resources whose arrival and consumption are subject to environmental randomness is an intrinsic process in both natural and artificial systems. This phenomenon can be modeled as a queuing process whose arrival distribution is determined by a search process with stochastic resetting. When the queuing system has a limited number of servers and the search process occurs within a bounded domain, the dynamics of expediting or delaying the search through stochastic resetting interact with the long-term dynamics of the number of resources in the queue. We combine results from queuing theory with those from search processes with stochastic resetting in a bounded domain to obtain regions of the parameter space of the search process that ensure convergence of the number of resources in the queue to a steady state. Furthermore, we find a threshold resetting rate at which the effects of stochastic resetting shift from reducing convergence regions to expanding them. Finally, we demonstrate that this threshold value grows exponentially with the number of servers, making it harder for stochastic resetting to improve the convergence of the queueing system.

We show that in classical spin systems, the precise nature of the late-time hydrodynamic tails of the autocorrelation functions of a generic observable is determined by (i) the dynamical critical exponent and (ii) the equilibrium thermodynamic properties of the corresponding observable. We provide numerical results for one- and two-dimensional systems and present theoretical considerations that only rely on the notion of ergodicity. Our result extends to the classical framework the relaxation-overlap inequality, first introduced in [Phys. Rev. X 15, 011059 (2025)] for quantum many-body systems satisfying the eigenstate thermalization hypothesis.