Fluctuating pairwise interactions are understood to drive fluidlike states in dense biological systems. These states find a broad range of functionalities, such as directing growth during morphogenesis and forming aggregates with heightened mechanical response. However, a tractable model capturing the role of microscopic fluctuating interactions in these structural transitions is crucially lacking. Here, we study a $p$-spin model with fluctuating pairwise couplings (of strength $D_a$ and persistence time $t_a$) as a schematic model for interaction-mediated fluidization. We find that while stronger fluctuations suppress the glass transition, more persistent fluctuations have the opposite effect. We identify the presence of an emergent fluctuation-dissipation relation at long times. We numerically extract the critical temperature $T_g(D_a,t_a)$ from a scaling relation near the transition, illustrating how microscopic fluctuations control the glass transition.

Higher-order interactions have recently emerged as a promising framework for describing new dynamical phenomena in heterogeneous contagion processes. However, a fundamental open question is how to understand their contribution from the perspective of the physics of critical phenomena. Based on a mesoscopic field-theoretic Langevin description, we show that (i) pairwise mechanisms such as facilitation or thresholding are formally equivalent to higher-order ones, (ii) pairwise interactions at coarse-grained scales govern the simplicial contact process and, (iii) the interplay between noise and topology is determined by the network spectral dimension. In short, we demonstrate that classical field theories, rooted in model symmetries and/or network dimensionality, capture the nature of the phase transition in real and synthetic networks.

We derive general trade-off relations between the power, efficiency, and constancy for two-terminal thermoelectric systems in the linear-response regime. Constancy, which quantifies the steadiness of the heat engine, is measured by its fluctuations. The bounds of the efficiency, power, and fluctuations are valid even when time-reversal symmetry is broken, revealing how such a symmetry breaking alters the fundamental constraints on steady-state energy conversion. Our results extend and refine previously established universal trade-offs, offering deeper insight into the performance limits in nonequilibrium thermodynamics. Guided by this bound, heat engines with broken time-reversal symmetry can be operated at near Carnot efficiency while maintaining finite power output and fluctuations, enabling them to outperform their traditional counterparts.

Anomalous diffusion and power-law distributions are observed in various complex systems. To provide a consistent dynamical foundation for these phenomena, we present a geometric derivation of the nonlinear Fokker-Planck equation by introducing the linearization principle directly at the dynamical stage. By identifying the generalized chemical potential as the natural dynamical ansatz, we construct a general thermodynamic framework where the drift term remains linear in the probability density, preserving the standard form of the Einstein relation. Within this framework, we show that the $q$-deformed geometry, corresponding to Tsallis statistics, exhibits a fundamental duality between the dynamic index $q$ and the thermodynamic index $2-q$: the stationary state is a $q$-Gaussian distribution that minimizes a free energy functional defined by a generalized entropy of index $2-q$. We prove the $H$ theorem for the derived equation and demonstrate its application to the harmonic oscillator and the free particle. This framework describes anomalous diffusion without relying on ad hoc constraints or phenomenological nonlinear drift forces.

We study overdamped stochastic dynamics confined by hard reflecting boundaries and show that the combination of boundary geometry and an anisotropic diffusion tensor generically generates directed motion. At the level of individual trajectories, the no-flux condition enforces an oblique reflection at the boundary, which produces a systematic drift parallel to the surface. The resulting local velocity takes the general form $v_B\left(\mathbf{x}\right)=\mathbf{t}{\left(\mathbf{x}\right)}^{\top }\mathbf{D}\mathbf{n}\left(\mathbf{x}\right)$, determined by the diffusion tensor $\mathbf{D}$ and the local boundary geometry encoded in the normal $\mathbf{n}$ and tangent $\mathbf{t}$. While this boundary-induced drift is local, it can accumulate into a macroscopic response, depending on the statistics of boundary encounters. We illustrate how this local boundary-induced drift gives rise to macroscopic transport using a minimal one-dimensional dimer composed of two particles with unequal diffusion coefficients. The repeated collisions act as reflections in configuration space and lead to sustained center-of-mass motion, including regimes of absolute negative mobility under constant forcing.

We study charge fluctuations of a family of stochastic charged cellular automata away from the deterministic single-file limit and obtain the exact typical charge probability distributions, known to be anomalous, using hydrodynamics. The cellular automata considered are examples of linearly degenerate systems where two distinct mechanisms of diffusion, namely, normal and convective diffusion, coexist. Our formalism, based on macroscopic fluctuation theory, allows us to describe current fluctuations stemming from these two diffusive processes, and we expect it to be applicable to generic linearly degenerate systems. The derived probability distributions match the exact microscopic result and numerical simulations.

Phenotypic plasticity enables prey species to develop inducible defences in response to predation risk, significantly influencing predator-prey interactions. In this study, we propose a nonlinear predator-prey model in which prey exhibit inducible defense mechanisms, while predators experience mutual interference described by a Beddington-DeAngelis functional response. The analysis reveals a stabilizing effect of prey defense on system dynamics. Interestingly, predator density increases with moderate levels of interference when prey defense is weak but declines monotonically as defense strength increases. When handling time is used as a bifurcation parameter, a bistable regime emerges, highlighting the importance of initial population densities. Extending the model to a spatial setting shows that stronger defences shrink the Turing instability domain. Furthermore, incorporating predator and prey taxis exerts an additional stabilizing effect by suppressing the formation of spatial patterns. These results emphasize the critical role of inducible defences and movement strategies in shaping both temporal and spatial ecological dynamics. Altogether, the model represents a nonlinear, nonequilibrium system where pattern formation arises from the interplay between reaction kinetics, diffusion, and cross-diffusion (taxis). The results contribute to the understanding of self-organization mechanisms in interacting particle-like systems with density-dependent interactions.

Edge-localized modes (ELMs) eject intense bursts of heat and particles that threaten plasma-facing components in fusion reactors. Nonlinear full-torus $\mathrm{BOUT}++$ simulations show that turbulence-driven zonal magnetic fields (ZMFs) play an essential role in nonlinear ELM evolution by maintaining self-consistent force balance. Zonal flows mitigate the initial crash through shear but do not prevent continued radial transport. When ZMFs are self-consistently included, turbulence-driven zonal currents modify the parallel current distribution and magnetic tension and are associated with a reduction of the axisymmetric ($n=0$) perturbed radial force imbalance. This coincides with a transition from convective, bursty propagation to more localized, diffusive transport. Similar behavior is observed across the regimes considered, including both resistive-ballooning and peeling-ballooning cases. Associated signatures, including radial electric field shear and parallel current redistribution, provide experimentally accessible diagnostics for present devices and ITER-relevant conditions.

Using particle-in-cell simulations to study nonrelativistic laser pulse propagation in an under-critical plasma, we identify a novel mechanism that occurs during the growth of turbulent magnetic loops: electron penetration heating. The loops have an electromagnetic left-hand chirality distinct from that of well-known quasistatic magnetic islands. The fast electrons penetrate through the loops and thus are accelerated to unexpected relativistic energies due to the symmetry breaking induced by the coupling between the loop field and the nonrelativistic electromagnetic wave. The identified features of penetration heating and magnetic loops might provide an alternative perspective for understanding superponderomotive electron heating in under-critical plasmas irradiated by nonrelativistic laser pulses. This is a potential explanation for anomalous hot electron generation in scenarios of laser-driven inertial confinement fusion.

The outflow velocity of expanding deuterium-tritium (DT) fuel can become significant after the bangtime, approaching local ion thermal velocity when the inertial confinement fusion (ICF) hotspot surpasses the ignition threshold. Under such conditions, the conventional assumption of an isotropic target-particle velocity distribution becomes questionable and the influence of bulk fluid motion on alpha-particle transport should be examined. In this paper we derive an analytical expression of the charged-particle stopping power in plasmas with arbitrary bulk fluid motion. We then apply this formalism to alpha-particle transport in an ICF hotspot. The results suggest that incorporating the background fluid velocity into the alpha-particle transport simulation results in a greater fraction of alpha-particle energy being transferred directly to the D and T ions, with a corresponding decrease in the energy deposited to electrons. These results indicate a potentially important correction to alpha-energy deposition in the post-bangtime hotspot.

Liquid lenses offer a versatile route to adaptive optics, but most existing implementations rely on mechanical deformation or high-voltage actuation, which limits scalability and long-term stability. Here, we demonstrate tunable liquid lenses based on magnetic body forces acting on optically transparent paramagnetic fluids. Spatial gradients of the magnetic field generate volumetric forces that reshape liquid interfaces in a controllable and reversible manner. Using a permanent ring magnet combined with a low-power electromagnet, we realize both concave lenses formed by a single paramagnetic liquid-air interface and compound convex lenses formed by a paramagnetic liquid coupled to an immiscible, nonmagnetic, higher-index liquid. We demonstrate experimentally, with good agreement with simulations, tunability of both types of liquid lenses and characterize their dynamic response and resolution limit. Because the actuation acts on the entire fluid volume, this approach is mechanically passive, electrically simple, and readily scalable, providing a promising platform for magnetically controlled adaptive liquid optics.

In light of the recent interest in finding multicritical behavior in stochastic systems, we compute the trajectory phase diagram of one-dimensional kinetically constrained models (KCMs), demonstrating the existence of dynamical phases separated by lines of self-duality. We further reveal that multicritical points delimit first-order from continuous active-inactive transition lines. For illustration, we consider four representative KCMs in detail: the domain-wall (DW), Fredrickson-Andersen (FA), the DW East, the ZZZ-FA, and the XOR-FA models. Via exact diagonalization and tensor network methods we achieve three goals: (i) we find that dynamical phases and their transitions can be related by duality arguments in a broad class of KCMs, (ii) we establish the presence of multicritical points on their self-dual lines, and (iii) we intertwine concepts related to dualities of quantum spin systems, classical stochastic dynamics, and large deviation theory.

Mathematical models of diffusion based on stochastic processes of the type of continuous-time random walks (CTRWs) are widely used for the description of various transport characteristics in complex media. An external or internal bias in a given CTRW model is often attributed to an asymmetric distribution of jump lengths, while the waiting times are assumed to possess identical distributions in all directions. However, for a number of real-world transport phenomena the latter assumption is violated. To account for such situations, we examine the properties of such biased CTRWs in one dimension. We propose a CTRW-based model of diffusion with the waiting-time distributions (WTDs) of the tracers chosen unequal for right- and left-directed jumps. Below we name CTRWs with such asymmetric WTDs (AWTDs) as ${\mathrm{A}}_t$-CTRWs. We derive the corresponding generalized Montroll-Weiss and master equations in Laplace and $Z$ space. We consider both exponential and power-law WTDs as the standard and most useful functional choices for the purposes of data analysis. For these two WTD classes, we analyze the average displacement (generally nonzero) and the mean-squared displacement of the diffusing particles and analytically compute the variance as effective statistical measures. Our analytical predictions favorably agree with the results of the performed computer simulations. Specifically, for a CTRW with power-law WTDs we find that at long times the emerging anomalous diffusion depends not only on the smallest exponent of the left- and right-directed WTDs. Such diffusion models can, e.g., be used to describe the anomalous diffusion in various anisotropic media in the presence of a drift. One hydrological example is a gravity-affected spreading of contaminants in porous rocks, a system where the CTRW-based models are widely known to be applicable. A biological example of a biased-CTRW-based transport is a regulated driven bidirectional transport of cargoes between the center of a living biological cell and its periphery taking place along the microtubule filaments.

We present a $Q$-learning framework for optimizing chemotherapy dosing schedules in a stochastic finite-cell model of tumor evolution under drug-induced selection. The tumor consists of three competing subpopulations: a chemosensitive lineage, $S$, and two single-drug-resistant lineages, $R_1$ and $R_2$, each resistant to one of two cytotoxic agents, $C_1$ and $C_2$. Drug administration is formulated as a discrete action space in a finite-state Markov process, where the state is defined by the composition $(S,R_1,R_2)$ constrained by a fixed population size $N$. Tumor volume evolves according to a separate growth equation, with expansion rate proportional to the difference between the population-averaged fitness and a fixed microenvironmental baseline. Using $Q$-learning, we derive optimal dosing policies that balance therapeutic pressure with the evolutionary dynamics of resistance. The reward function is engineered to promote long-term coexistence among subpopulations, thereby delaying fixation of resistance by penalizing population imbalance. We analyze the structure of the optimal policies to (i) infer dominant evolutionary trajectories under treatment, (ii) quantify robustness to partial observability of both initial conditions and state updates, and (iii) construct simplified, symmetry-informed heuristics that approximate the full learned policy. Our results highlight the potential of model-free adaptive control strategies to steer tumor evolution away from drug resistance in the presence of biological stochasticity and information constraints.

We present an exchange Monte Carlo (EMC) method designed for application in continuous-space path integral Monte Carlo (PIMC) simulations at finite temperature. Traditional PIMC methods for bosonic systems suffer from long autocorrelation times, particularly when measuring observables affected by particle permutations, such as the winding number. To address this issue, we introduce an exchange update scheme that facilitates replica transitions between different interaction regimes, significantly accelerating Monte Carlo dynamics—especially for global observables sensitive to permutation effects. Furthermore, we incorporate stochastic potential switching (SPS) to efficiently decompose interactions, substantially enhancing computational efficiency for long-range interatomic pair potentials such as the Lennard–Jones and Aziz potentials.

We summarize the salient features of our theory of nonphononic vibrational excitations in glasses [W. Schirmacher et al., Nat. Commun. 15, 3107 (2024)]. Next, we provide further evidence of the nonuniversality of the ${\omega }^4$ scaling of the nonphononic vibrational density of states (DoS), and the existence of an important class of nonphononic excitations in glasses, which we call defect states. These modes are induced by frozen-in stresses and can be classified as quasilocalized. Our results suggest that the commonly observed low-frequency ${\omega }^4$ scaling of the nonphononic vibrational density of states is highly dependent on the technical aspects of the molecular dynamics simulations employed to compute the DoS.

We derive exact critical-temperature bounds for the classical ferromagnetic Ising model on two-dimensional periodic tessellations of the plane. For any such tessellation or lattice, the critical temperature is bounded from above by a universal number that is solely determined by the largest coordination number on the lattice. Crucially, these bounds are tight in some cases, such as the honeycomb, square, and triangular lattices. We prove the bounds using the Feynman–Kac–Ward formalism, confirm their validity for a selection of more than 200 lattices, and construct a two-dimensional lattice with 24-coordinated sites and a high critical temperature.

The spatial organization of individuals and their interactions in communities are important factors known to preserve diversity in many complex systems. Inspired by metapopulation models from ecology, we study opinion formation using a network-based approach in which nodes represent communities of interacting agents holding one of two competing opinions, and links represent avenues of migration. Agents adapt to the dominant opinion within a community or migrate toward other communities. Using a master stability function approach, we analytically derive conditions for diffusion-driven pattern formation and identify structural features of the community network that sustain opinion diversity. Our model shows that even under minimal opinion rules, the interaction between local dynamics and community structure generates spatial patterns that allow minority opinions to persist by gaining local dominance.

We investigate how much bias in the initial configuration is required to drive global agreement in synchronous, deterministic majority dynamics on large random $d$-regular graphs. Nodes take values $\pm 1$ and update their states at each discrete time step to align with the majority of their neighbors. Using the backtracking dynamical cavity method (BDCM), we estimate the minimal fraction of initial $+1$ nodes required to achieve a $+1$ consensus in $p$ time steps. Our analysis predicts that for $d\ge 4$ an initial global minority of $+1$ nodes is sufficient to quickly steer the entire system toward consensus on $+1$. We then investigate whether such initial conditions can be determined explicitly for a given large random regular graph. To this end, we introduce a new algorithm, which we name history-passing reinforcement (HPR), designed to find such initial configurations with a minority of $+1$ nodes. We find, as a main result, that the HPR algorithm finds initial configurations where the minority takes over the majority for $d$-regular random graphs with $d\ge 4$. The HPR algorithm outperforms standard simulated annealing-based methods but does not reach the lowest densities predicted by the BDCM. Rather, the lowest density achievable by the algorithm is near the onset of a dynamical one-step replica symmetry-breaking phase, which we estimate using a one-step replica symmetry-breaking formulation of the BDCM. While we focus on the majority dynamics and random $d$-regular graphs, the algorithm can be extended to other dynamical rules and classes of sparse graphs.