The spatial structure of populations may promote the emergence and maintenance of cooperation. Cooperation in the prisoner's dilemma is favored under specific update rules in evolutionary graph theory models with one individual per node of a graph, but this effect vanishes in models with well-mixed demes connected by migrations under soft selection (each deme contributing independently of its productivity). In contrast, experiments and models involving cycles of growth, merging and dilution have shown that spatial structure can favor cooperation. Here, we reconcile these findings by studying deme-structured populations under growth-merging-dilution dynamics, corresponding to a clique (fully connected graph) under hard selection (each deme contributing in proportion to its productivity). We obtain analytical conditions for the cooperator fraction to increase during deterministic logistic growth, and to increase on average under dilution-growth-merging cycles, in the weak selection regime, where fitness differences between genotypes are small. Furthermore, we analytically express the fixation probability of cooperators under weak selection, yielding a criterion for cooperators to have a higher fixation probability than neutral mutants. Finally, numerical simulations show that stochastic growth further promotes cooperation. Overall, hard selection is essential for cooperation to be promoted in deme-structured populations.

In thermodynamic equilibrium, the fluctuation-dissipation theorem links thermal fluctuations and dissipation. Biological systems, however, are driven out of equilibrium by internal processes that produce additional, active fluctuations. Despite being relevant for biological functions such as intracellular transport, predicting the statistical properties of active fluctuations remains challenging. Here, we address this challenge in a minimal model of an active gel as a network of elastic elements connected by transient cross-linkers. The cross-linkers' binding and unbinding rates break detailed balance, which drives the system out of equilibrium. Through coarse-graining, we derive fluctuating hydrodynamic equations including an active noise term, which emerges explicitly from the breaking of detailed balance. Finally, we provide predictions for the stochastic motion of a tracer particle embedded in the active gel, which enables comparisons with microrheology experiments both in synthetic active gels and in cells. Overall, our work provides an explicit link between the statistical properties of active fluctuations and the molecular breaking of detailed balance. Thus, it paves the way toward complementing the fluctuation-dissipation theorem with a fluctuation-activity relation in active systems.

Dipolar fluids are known to exhibit complex self-assembly at low temperatures, yet a compact thermodynamic description of their aggregate statistics has remained elusive. Using molecular dynamics simulations of Stockmayer particles with a purely repulsive WCA core, we confirm that over broad regions of the $(\rho ,T)$ phase space the chain-size distribution follows an exponential decay with characteristic size $s_0$. Within this regime, we find that $s_0$ can be accurately described by an effective free energy $\varphi$ that incorporates translational entropy, bonding energy, and a crowding penalty. Identifying deviations from this ideal scaling provides a further division of the phase space into four regions. Therefore, our results locate a regime of relatively simple chain statistics and offer an alternative regime-based perspective on dipolar self-assembly.

We determine the complete phase structure of the frustrated Ising model with competing nearest-neighbor, next-nearest-neighbor, and four-spin plaquette interactions, using real-space renormalization on four members of hierarchical square lattices characterized by their coarse-graining scales. The construction yields exact fixed points and critical exponents for paramagnetic, ferromagnetic, Néel (antiferromagnetic), and striped phases, meeting at a multicritical fixed point. We show that the full frustrated phase topology emerges only for odd coarse-graining scales, identifying the minimal geometry required to resolve independent frustrated ordering channels and revealing a parity-controlled mechanism absent in the unfrustrated model. Order parameters and coupled fields are also introduced to enable a determination of the scaling behavior of the different critical and multicritical points in the phase diagram.

The largest connected component in duplication-divergence growing graphs with symmetric coupled divergence is studied. Finite-size scaling reveals a phase transition occurring at a divergence rate ${\delta }_c$. The ${\delta }_c$ found is close to the locus of zero in Euler characteristic of finite-size graphs known to reflect the proximity of the largest connected component transition. A close correspondence with the vanishing of a scaling relation exponent for moments of the vertex degree distribution is shown, with such a scaling relation that generalizes a known form for duplication-divergence model graphs. The role of noninteracting vertices in shaping this transition with their presence or absence in duplication is also considered through a particular relation which would result in the two cases being comparable. The findings have relevancy for bond percolation in these growing graph models.

We develop an energy-based theoretical framework to predict jet morphologies in electrospinning. The charged polymer jet is modeled as a one-dimensional elastic curve subjected to a uniform electric field. The model includes the external-field energy, an effective local representation of curvature-dependent electrostatic self-interaction, and the bending and torsional elastic energies of the viscoelastic jet. To address the mathematical complexity arising from torsional effects and three-dimensional geometry, the resulting Euler-Lagrange equations are solved using physics-informed neural networks (PINNs). The model identifies three distinct morphological regimes governed by the competition between electrostatic and mechanical energies: a straight configuration at low stiffness, a three-dimensional spiral at intermediate stiffness, and a planar spiral at high stiffness. The predicted spiral envelopes are consistent with the experimental trend and show better agreement than the predictions of a previous force-balance model. This work provides a unified energetic interpretation of electrospinning jet morphologies and highlights the potential for integrating physics-based modeling with machine learning for complex electrohydrodynamic systems.

Self-interacting jump processes (SIJPs) describe systems with non-Markovian stochastic dynamics in which transition rates depend on empirical observables of the process, which gives rise to long-range memory and feedback. We derive the “level-2.5” large deviation (LD) principle governing the joint fluctuations of empirical occupation measure and the flux matrix for a broad class of SIJPs with general functional dependence on an empirical observable. The derivation is based on an exponential tilting construction and reveals a separation between a faster timescale of the microscopic dynamics and a slower timescale of the memory-driven evolution of transition rates, which is expressed through an exponentially discounted LD rate functional. Using this variational framework, we derive kinetic and thermodynamic uncertainty relations that extend classical Markovian bounds to non-Markovian systems and illustrate their performance with simple examples.

Genuinely critical dynamics have been proposed to organize many natural and social systems, yet exact criticality is usually thought to preclude stationarity because the mean activity diverges. I show that this conclusion is not generally valid for self-exciting Hawkes point processes. At criticality, stationarity in law is controlled not by the mean intensity but by local finiteness of the infinite-past Poisson-cluster construction. The relevant quantity is the fixed-window hitting probability $H_T\left(u\right)$, the probability that a cluster born at time $-u$ contributes at least one event to a window of length $T$. For offspring waiting-time tails $\mathbb{P}(S>t)\sim t^{-\theta }$ and fertility tails $\mathbb{P}(\kappa >x)\sim x^{-\gamma }$, a finite-mean-lifetime argument rigorously establishes stationarity for $1<\gamma <2$ and $\theta >\gamma$, while the finite-memory, finite-variance critical regime is nonstationary. A direct asymptotic analysis of the exact fixed-window nonlinear renewal equation identifies the precise local-finiteness boundary $\theta =\gamma -1$ in the infinite-fertility-variance regime. Below this boundary, $H_T$ is nonintegrable. At the marginal point $\theta =\gamma -1$, a refined Laplace-Tauberian analysis yields $H_T\left(u\right)\sim \frac{{[lnu]}^{1/(\gamma -1)}}{u}$, which is also nonintegrable, demonstrating that the critical Hawkes process remains nonstationary at the boundary $\theta =\gamma -1$. Direct numerical solutions of the exact renewal equation confirm the predicted power-law and logarithmic regimes across the transition. Thus broad fertility fluctuations can sustain a locally finite stationary critical Hawkes process with positive immigration even though its stationary mean intensity is infinite.

We consider the application of the fluctuation dissipation theorem to the electrodynamics of Aharonov-Bohm, which differs from Maxwell's electrodynamics in that it allows for local nonconservation of charge. For the case of a system of nonconserved charges at thermal equilibrium we obtain the same spectral distribution of energy of the electromagnetic field as in Maxwell electrodynamics. However, the electric field contribution to that energy doubles that in the Maxwell case, while the magnetic contribution is the same as in Maxwell theory; the electric excess energy is compensated by a negative contribution arising from the Aharonov-Bohm scalar field. For a conductor with local nonconservation of charge described by the $\gamma$ model, we derive the spectrum of current correlation at first order in $\gamma$, which results in a violet noise contribution added to the classical Johnson-Nyquist white noise result for the voltage fluctuations in a conductor.

The weakly first-order nature of the two-dimensional five-state ferromagnetic Potts model poses challenges for numerical study. Using density-matrix and tensor-network renormalization-group methods, we investigate these transitions of the $q$-state Potts model via the Klein bottle ratio $g$ on original and dual lattices. Finite-size scaling of $g$ as a function of transverse system size $L_y$ accurately locates the critical points for $q=3,4,5,6$. We further examine the transfer-matrix spectra and entanglement entropy, extracting central charges through toroidal and Klein bottle boundary conditions. For $q=5$, the extracted central charge ($c\approx 1.14811$) is close to the real part of the theoretical value $c_{5\text{-Potts}}=1.1375\pm 0.0211i$ predicted by complex conformal field theories (CFTs). The observed drift in the scaling exponent $b$ effectively distinguishes the continuous transition from the weakly first-order regime. Furthermore, the extrapolated divergence of $g$ confirms the first-order character of the $q=5$ Potts model, while for the $q=4$ model, both the CFT-predicted eigenvalue distribution and the logarithmic corrections are numerically verified.

We examine the spectral properties of a Stuart-Landau oscillator with state-dependent time-delayed feedback in the presence of amplitude and phase noise. We demonstrate that an asymmetric Fano resonance profile appears in the spectrum under amplitude noise, due to amplitude-phase coupling caused by the state-dependent delay. Conversely, this asymmetry is absent in the presence of phase noise.

Reservoir computing (RC) excels at chaotic time series prediction but suffers from high sensitivity to hyperparameters (spectral radius, sparsity) and requires large reservoirs, limiting its utility. To overcome these limitations, we propose an enhanced RC framework that introduces time-shift transformations on the reservoir states to embed temporal information, followed by explicit Volterra-style nonlinear feature expansions—quadratic polynomial expansion (QT-RC) or hierarchical product expansion (HP-RC). These methods capture multiplicative nonlinearities and historical information while preserving the efficiency of linear ridge regression. Using the Lorenz and Rössler systems as benchmarks, we show that our methods achieve prediction accuracy comparable to traditional RC with hundreds of nodes while using only five to 10 reservoir nodes, and drastically reduce sensitivity to spectral radius and connectivity. Phase diagram analysis reveals complementary roles: nonlinear transformations enhance expressiveness and reduce spectral radius dependence, whereas time-shift transformations improve robustness under dense connectivity. This work offers a pathway toward efficient, robust, and hardware-friendly reservoir computing, grounded in Takens' embedding theorem and Volterra series theory, which provides a universal framework for nonlinear systems with fading memory.

The study of homophily in networks usually involves investigating whether nodes have a tendency to make more direct connections with similar nodes than what would happen in a random network. However, the study of homophily between nodes that are not directly connected is also of interest. Remarkably, even though there is a vast literature on long-range degree homophily, just a few works have investigated other properties, but only considering linear relations among scalar attributes of the nodes. In this work, we put forth a measure of long-range homophily that can deal with nonscalar and noncategorical node attributes and enables the analysis of nonlinear relations. This measure can be viewed as an extension of the usual Newman assortativity, as it is based on the comparison of the similarity of node attributes in a given network to that expected in a nonhomophilic network where connections are randomly made while preserving node degrees. We show the application of the measure in a few real-world examples, some of which exhibit a nontrivial long-range homophilic behavior.

A unified theoretical framework is given to rigorously describe the hierarchy of macroscopic equations recovered from the Boltzmann model equation. The framework first integrates the Chapman-Enskog (CE) analysis with the Hermite expansions of the equilibrium distribution function. The framework is then augmented by a Hilbert expansion of the Hermite coefficients with respect to the relaxation time. This additional step removes an implicit assumption in existing analyses [X. Shan et al., J. Fluid Mech. 550, 413 (2006)], namely that all Hermite coefficients share the same relaxation time order, which limits the applicability of the Boltzmann model equation for some existing kinetic models and is inconsistent with the multiscale asymptotics underlying the CE analysis. Within the present formulation, a richer kinetic hierarchy can be constructed, in which different Hilbert coefficients correspond to distinct moment equations, providing a systematic route for recovering generalized macroscopic equations. To demonstrate the applicability of our proposed framework, a general form of the kinetic model is analyzed for incompressible flows, encompassing four representative models from the literature together with an additional model derived within the present framework. The proposed model introduces an oscillation-suppression term in the Hilbert coefficients, yielding a continuity equation that combines features of artificial compressibility and penalty methods. This modification effectively suppresses spurious pressure without introducing additional auxiliary variables. Simulations of decaying turbulence confirm the theoretical findings and demonstrate the effectiveness of the proposed model.

Classical resistive tearing theory assumes a prescribed current-sheet equilibrium, but a finite normal magnetic field can evolve the background on the tearing timescale. For a transversely pressure-balanced Harris profile of initial half-thickness $a$ and asymptotic reconnecting-field magnitude $B_0$, threaded by uniform $B_n$ ($\xi \equiv B_n/B_0$), we derive an exact evolution in ideal magnetohydrodynamics: counterpropagating Alfvénic fronts broaden the neutral layer and generate a sheet-parallel flow with velocity gradients on its two flanks. The same normal field enters the linearized perturbation equations directly through ideal transport, alongside advection and flow-curvature terms from the evolving velocity profile. Inner-layer estimates recover ${\xi }_{\mathrm{crit}}\sim S^{-3/4}$ for the breakdown of the resistive balance at the classical fastest-growing scale, where $S$ is the Lundquist number based on $a$. Numerical frozen-profile calculations show that growing modes can persist after central resistive dominance is lost; eigenfunction comparisons at fixed wave number and predominantly Doppler-shifted propagation support a normal-field-modified continuation of classical tearing. The normal field supplies no net perturbation energy. Energy extraction from the reconnecting-field gradient dominates at small and moderate widths and weakens as the sheet broadens. The velocity-gradient contribution becomes comparable only in broad, weakened modes, where it partly offsets the loss without reversing the decline in growth. For the representative case $S={10}^6$, magnetic Prandtl number ${\mathrm{Pr}}_m=0$, and $\xi ={10}^{-4}$, the maximum growth rate falls by a factor of about ten from its initial value when the neutral-layer half-width $w$ reaches $w/a\simeq 1.59$, where the growth and broadening times become equal. Only about 0.18 additional upper-envelope e-folds are estimated between this crossing and $w/a=2$, where the growth rate is about 25 times smaller than its initial value, and the instantaneous spectrum remains unstable. These results support dynamical suppression of further linear amplification over the sampled evolution, while nonlinear island or plasmoid formation remains unresolved. Current-sheet disruption criteria must therefore account for both direct modification of the inner balance and normal-field-driven background evolution.

Prompted by early experimental realizations of plasma-optical components, we examine how finite formation times affect the quality and scaling behavior of a plasma grating induced by the ponderomotive potential of two counter-propagating pump laser beams. Ponderomotively driven gratings provide an alternative to ionization gratings, which offer significant advantages in terms of stability and contrast, but exhibit notable drawbacks regarding repetition rates and material modification. Here, in addition to parameters discussed in prior work, we identify the pump pulse duration ${\tau }_p$ as another factor for the dynamics and persistence of ponderomotively driven plasma gratings. Based on full Vlasov simulations we predict the maximum density grating amplitude as well as its lifetime as a function of electron temperature $T_e$ and laser pulse duration ${\tau }_p$. For interpretation and modeling, we use a generalized form of a known one-frequency kinetic model to a finite-bandwidth scenario. Based on these investigations we predict the influence of ${\tau }_p$ and $T_e$ on the maximum achievable grating performance, providing a detailed explanation of the observed grating scaling. As a general result, we find that even gratings generated by laser pulses of less than a few hundred femtoseconds duration ${\tau }_p$ allow for very efficient utilization up to picoseconds, provided that the plasma temperature is not too high (e.g., $T_e\le 100\mathrm{eV}$).

Quantum batteries (QBs) represent a promising and emerging class of energy storage devices that exploit the principles of quantum mechanics to achieve superior performance compared to conventional, classical batteries. In this work, we investigate the charging dynamics of a QB in a bipartite system composed of two qubits, where one qubit acts as a charger and the other as the battery, each embedded in an independent cavity reservoir. The model incorporates multiphoton atom-cavity interactions as well as quenched disorder (QD) in the system-reservoir coupling, including discrete, uniform, Gaussian, and Cauchy-Lorentz distributions. The resulting dynamics are analyzed in both weak- and strong-coupling regimes. We examine how the multiphoton order affects the internal energies of the charger and the battery, and show that increasing the multiphoton order leads to enhanced dissipation and a reduction of the energy transferred to the battery. By comparing different disorder statistics, we find that uniform and discrete QDs can partially mitigate decoherence and yield higher charging efficiency compared to Gaussian and Cauchy-Lorentz QDs. Furthermore, our results demonstrate that strong system-reservoir coupling induces non-Markovian dynamics accompanied by rapid energy loss and suppression of ergotropy and efficiency. In contrast, efficient charging and partial revival features are predominantly observed in the weak-coupling, Markovian regime, where coherent dynamics are preserved.

The fluctuation theorem (FT) relates microscopic trajectory distributions to macroscopic averages. Using quasiprobability trajectories, this framework has recently been extended to quantum information dynamics. Despite sharing the form of conventional thermodynamic FTs, information FTs involve quasiprobabilities whose negativity and statistical properties remain poorly understood. In this work, we analytically determine the properties of negative distributions for two-qubit Bell-diagonal states evolving under local dephasing, depolarizing, and amplitude-damping channels, under the fixed local computational basis. We show that the occurrence of negative quasiprobabilities is not determined by the entanglement or Bell nonlocality of the initial state. For these channels, a diagonal-interference decomposition identifies a nonnegative reference contribution and yields channel-dependent interference bounds. More importantly, we prove that quasiprobability distributions containing negative weights can violate Horváth's necessary and sufficient criterion for the Jensen-Steffensen inequality to hold for every continuous convex function, even though the specific exponential Jensen-like relation enforced by the FT and the quantum data-processing inequality remains valid. This trajectory-level contrast with classical stochastic descriptions reveals a distinctive feature of quantum information dynamics that is invisible when only the corresponding average-level information inequalities are considered.

Visual alignment is an intrinsic physical property of certain active matter. Cumulative evidence indicates that active particles with visual alignment exhibit unique nonequilibrium dynamics, including aggregation, migration, and vortex motion. These collective behaviors can reshape their surrounding living environments. Based on this property of active matter, we design a foraging scenario and establish a mixing system including two categories of active particles: visually aligned and nonvisually aligned active particles. Nutrients are injected into the system to enable free competition between the two particle types, aiming to investigate their independent motion characteristics and competitive performance in resource foraging. Simulations reported that visually aligned active particles possess inherent competitive advantages over nonvisually aligned counterparts in nutrient competition. The nutrient-region accumulation can be maximized by appropriately regulating parameters such as system density, resource scarcity level, visual alignment strength, and particle softness. We analyze the mean-squared displacement and local synchronization rate to reveal the underlying physical mechanism. Visually aligned active particles enhance interparticle cooperation, which compensates for the decline in individual diffusion ability and further raises resource harvesting efficiency. This work provides different insights into how limited visual perception modulates the competitive dominance of active matter systems.

We study the scaling properties of long-range loop-erased random walks (LR-LERW), where the underlying random walker performs Lévy-flight-like jumps with a power-law step-length distribution $P\left(\mathbf{r}\right)\sim {\left|\mathbf{r}\right|}^{-(d+\sigma )}$. Using extensive Monte Carlo simulations, we measure the scaling relation $N\sim R^{d_N}$ between the loop-erased step number $N$ and the spatial extent $R$, and determine the geometric exponent $d_N$ for various values of $\sigma$ in spatial dimensions $d=1,2,$ and 3, as well as at the marginal point $\sigma =2$ in $d=4$ and 5. We observe a continuous crossover from long-range (LR) to short-range (SR) behavior as $\sigma$ increases. Below the upper critical dimension $d<d_c=4$, for $\sigma <d/2$, loop erasure is asymptotically irrelevant and $d_N=\sigma$, consistent with Lévy-flight scaling. For $d/2<\sigma <2$, loop erasure becomes relevant and $d_N$ varies continuously toward the short-range loop-erased random walks value. At the marginal points with $\sigma =d/2$ or $\sigma =2$, clear logarithmic corrections are observed. At and above the upper critical dimension, $d\ge 4$, the scaling at $\sigma =2$ is found to be $N\sim R^2/lnR$, consistent with that of the corresponding Lévy flight. Our results provide a systematic numerical determination of $d_N\left(\sigma \right)$ for the LR-LERW across dimensions, and are consistent with ${\sigma }_{*}=2$ as the boundary between LR and SR critical behaviors recently established in a broad variety of statistical models.