We study finite-time quantum Otto cycles whose working medium is a harmonic oscillator undergoing quantum Brownian motion described by the Caldeira-Leggett model when the oscillator is in contact with heat baths in isochoric processes. The time evolution of the Otto cycle is studied by analytically solving the exact Heisenberg-Langevin equations for the system variables and the interaction energy between the system and the bath. This enables us to investigate non-Markovian strong-coupling effects on the quantum Otto cycle. We obtain cyclic steady states and study the thermodynamic properties of the Otto cycle for various values of the parameters describing the heat baths and the coupling between the system and the bath. We compare our results with those obtained in the Markovian limit, where the time evolution is described by the Lindblad equation. We find that the change in the interaction energy during the isochoric process contributes to both work and heat and plays a crucial role in determining the thermodynamic behavior of the cycle. This is in contrast to the behavior of the state observables of the working medium, which show relatively small changes compared to the Markovian counterparts. We find that non-Markovian effects only become significant when we consider thermodynamic fluxes such as work and heat with the system-bath interaction fully taken into account. We also compare our results with the power-efficiency trade-off relation recently proposed for the Markovian quantum Otto engine.

A graph-theoretic analysis of the steady-state current noise in master equations under a finite thermodynamic force (affinity) is presented. The incidence matrix twisted by a finite affinity is not orthogonal to the standard cycle space, motivating the introduction of twisted circuit matrices to restore the orthogonality. The resulting twisted-cycle matrix yields an interferencelike effect, enabling us to express the signal-to-noise ratio as a quadratic optimization problem in terms of twisted-cycle currents. We apply this framework to a Brownian computation model on a treelike state-transition diagram with exponential backward branching, finite affinity at each step, and a single reset cycle. In the limit of an infinitely long intended computation path $\ell$, the Fano factor of the reset current undergoes a transition from noiseless to Poissonian behavior at an affinity equal to the logarithm of the number of immediate predecessors $\alpha$. This corresponds to an easy-hard transition in the computational time complexity [K. Okajima and K. Hukushima, arXiv:2512.24728], which is not captured by the thermodynamic uncertainty relation. This transition point precisely characterizes the thermodynamic costs of logically irreversible computation: in the absence of affinity, the reset cost scales as $ln\ell$, whereas reaching the transition point requires a thermodynamic force of order $ln\alpha$ per step to counteract backward branching.

Phyllotactic patterns, i.e., the arrangements of organs around a stem in some plants, represent not only fascinating geometries but also a source of inspiration for advanced biomimetic technological applications. Recently, spatial symmetry-breaking instabilities have been shown to feature, in some cases, phyllotactic symmetries when the radial growth of the pattern is slaved to a reactive front. We show here that phyllotactic ordering can also emerge when a homogeneous system is unstable with respect to a spatially self-organizing instability, and pattern formation is triggered by a localized perturbation that propagates radially. To do so, we numerically investigate the emergence of phyllotactic patterns from two different spatial symmetry-breaking instabilities coupled to radial growth in supercritical conditions: a far-from-equilibrium Turing instability studied here with the Brusselator model and equilibrium spinodal decomposition modeled by the Cahn-Hilliard equation. In both cases, radial expansion of the perturbations leads to the formation of concentric rings that subsequently fragment into spots, generating highly symmetric phyllotactic arrangements. The resulting patterns belong to the family of whorled modes, characterized by equal numbers of clockwise and counterclockwise parastichies. The morphologies are robust under variations of the characteristic wavelength and exhibit self-similarity when rescaled by this intrinsic length scale. A geometric analysis reveals that phyllotactic order arises from a space-optimization hexagonal lattice packing, as confirmed by Voronoi diagrams and representations in rescaled polar coordinates. Despite the common lattice structure, the two instabilities may select different orientations of propagation with respect to the radial direction. These results confirm the radial growth of spatial symmetry-breaking systems as a universal mechanism able to generate phyllotactic order.

We consider temporal networks that are a union of disjoint cliques at all times $t$. We call temporal networks that consist of disjoint cliques temporal clique graphs. We extend the exact solution of mean-field SIS epidemics with self-infections on the complete graph, derived by Prasse et al. [Chaos 31, 063115 (2021)], to all temporal clique graphs. Temporal clique graphs cover a range of commonplace models of network dynamics, including metapopulation models and specifically random-walker-induced temporal graphs. Since the exact solution of mean-field SIS on temporal clique graphs is piecewise (i.e., given by different functions on different intervals), we apply further approximations and find an approximate expression for the expected fraction of infected individuals, called the prevalence $y\left(t\right)$, at all times $t$, with as parameters only the infection rate $\beta$, the curing rate $\delta$, and the average size ${\theta }_j$ of each clique $j$ in the steady state of the network dynamics. Our strongest assumption is that the contact network is static and in its steady state, effectively ignoring all graph dynamics. Despite the drastic assumptions, in ignoring any temporal aspects of the contact network, the approximation is remarkably accurate, when the number of walkers is high. We assess our prevalence approximation (15) and indicate and explain its accuracy.

The graphicality problem—whether or not a sequence of integers can be used to create a simple graph—is a key question in network theory and combinatorics, with many important practical applications. In this work, we study the graphicality of degree sequences distributed as a power law with a size-dependent cutoff and as a double power law with a size-dependent crossover. We combine the application of exact sufficient conditions for graphicality with heuristic conditions for nongraphicality which allow us to elucidate the physical reasons why some sequences are not graphical. For single power laws we recover the known phase diagram, we highlight the subtle interplay of distinct mechanisms violating graphicality and we explain why the infinite-size limit behavior is in some cases very far from being observed for finite sequences. For double power laws we derive the graphicality of infinite sequences for all possible values of the degree exponents ${\gamma }_1$ and ${\gamma }_2$, uncovering a rich phase diagram and pointing out the existence of six qualitatively distinct ways graphicality can be violated. The validity of theoretical arguments is supported by extensive numerical analysis.

In this work, we study the dynamics of multiple random walkers on networks subject to a simultaneous resetting protocol, whereby all walkers are synchronously returned to their respective initial nodes. For this collective Markovian process, we derive exact analytical expressions for the mean first-encounter time, defined as the average time required for all walkers to meet for the first time at a given node. These results are formulated in terms of the eigenvalues and eigenvectors of the transition matrices governing the dynamics without resetting, providing a clear spectral interpretation of the impact of resetting on encounter processes. We further establish a general criterion for finite networks that determines when the introduction of a nonzero resetting probability reduces the mean first-encounter time and leads to an optimal resetting strategy. The theoretical predictions are illustrated through numerical results on regular and heterogeneous networks, for encounters involving two or more walkers, and for combinations of local and nonlocal dynamics. Our findings demonstrate that simultaneous resetting can significantly reduce encounter times for specific target nodes and initial conditions, while becoming ineffective for highly exploratory dynamics or distant targets. A comparison with independent resetting shows that simultaneous resetting is more efficient in homogeneous networks, whereas independent resetting can outperform it in heterogeneous structures, thereby revealing a trade-off between synchronization and exploration. The framework provides a unified approach to collective search and encounter problems on networks with resetting.

Cancer cells show global changes in chromatin structure that lead to stable alterations in gene expression and potentially other nuclear functions. Small-angle neutron and x-ray scattering (SAXS) is one of the most informative and direct ways to study the chromatin structural organization on nanoscales and microscales. SAXS studies of the chromatin in the nuclei of a fibroblast (DF-2 cell line), the nuclei of a fibrosarcoma (HT-1080 cell line), and the nuclei of a carcinoma (A549 cell line) have been reported. The scattering intensity from DF-2 cell nuclei is described by cubic law ($Q^{-3}$) in the momentum transfer range from 0.05 to $0.5{\mathrm{nm}}^{-1}$ that corresponds to scattering from logarithmic fractal structure of channels which form the internal transport system of the nucleus. A different approach to processing experimental data is presented, involving the subtraction of the contribution from the intranuclear system of transport channels ($Q^{-3}$) from the total scattering intensity, which allows visualization of chromatin structures located inside the system of transport channels. Analysis of SAXS data for HT-1080 cell nuclei and A549 cell nuclei showed the presence of a large number of 30-nm supernucleosome structures of decompacted chromatin inside the logarithmic fractal structure of the transport system of the nucleus.

Speckles, or laser hot spots, are the intensity maxima of optically smoothed laser beams that seed instabilities, making a quantitative statistical description of speckles of interest. Earlier statistical theories estimated the number of speckles above an intensity level set for optically smoothed beams produced by random phase plates, using an ansatz that relates intensity maxima to the maxima of the real and imaginary components of the underlying complex Gaussian electric field. Here, we count speckles directly from the laser intensity field, treating it as a ${\chi }_2^2$ random field and imposing the local maximum conditions without a single-component ansatz. We evaluate the theory for square, circular, annular, and Gaussian aperture spectra, and include induced spatial incoherence as a temporal smoothing mechanism. Monte Carlo simulations confirm the theory and show improved accuracy relative to the earlier ansatz-based formulation. Applications include a simple stimulated Brillouin scattering reflectivity model using the resulting speckle statistics, and a comparison between speckle-driven and thermal noise density-fluctuation spectra.

The inverse-power soft-sphere model provides a controlled platform for tuning the range and softness of purely repulsive interparticle interactions through the exponent $n$, with the hard-sphere limit recovered as $n\to \infty$. While the bulk thermodynamics and solid-liquid interfacial free energies of this model system have been extensively characterized, the corresponding excess interfacial stress and its dependence on interaction softness remain largely unexplored. In this work we perform molecular dynamics simulations to quantify the reference excess interfacial stress ${\tau }_1$ of equilibrium face-centered-cubic soft-sphere solid-liquid interfaces for the (100), (110), and (111) orientations over a broad range of inverse-power exponents, $n=6–100$, together with a model-dependent continuation of the finite-$n$ branch to $s=1/n=0$. Here the subscript 1 denotes quantities evaluated at the reference coexistence state $T_{\mathrm{m}}^{*}=1$, from which values along the corresponding coexistence line can be generated by inverse-power scaling. The pressure tensor profiles reveal that the normal component remains consistent with mechanical equilibrium in the bulk phases, whereas the lateral pressure components exhibit pronounced orientation- and softness-dependent redistribution in the interfacial region. As a result, ${\tau }_1$ displays a much stronger dependence on $1/n$ and crystallographic orientation than the reference solid-liquid interfacial free energy ${\gamma }_1$. In particular, ${\tau }_1$ changes sign for the (100) orientation as the repulsion becomes steeper, whereas the (110) and (111) interfaces remain predominantly compressive and become increasingly negative toward the hard-sphere side. After removing the solid-density area scale $k_{\mathrm{B}}T{\rho }_{\mathrm{s}}^{2/3}$, the softness dependence of ${\gamma }_1$ is substantially reorganized, whereas the stress sign reversal and the increasingly compressive (110) and (111) trends persist. This density-scaled comparison shows that the principal stress trends arise from interfacial stress redistribution rather than from the change in bulk density alone. By combining the present stress data with the benchmark interfacial free energies ${\gamma }_1$ of Davidchack and Laird [Phys. Rev. Lett. 94, 086102 (2005)], we further form cross-study reference combinations ${\tau }_1-{\gamma }_1$, which are negative for all orientations and substantially more anisotropic than ${\gamma }_1$ itself. These results provide a softness-resolved benchmark for interfacial thermodynamics in a purely repulsive model system and establish excess interfacial stress as a sensitive mechanical probe of solid-liquid interfacial structure beyond the interfacial free energy alone.

We investigate heat transport through a central harmonic chain coupled at its ends to two identical harmonic leads, which serve as heat reservoirs, within the nonequilibrium Green's function formalism. The central chain and the leads are characterized by different masses and spring constants, while the interfacial coupling $\tau$ is treated as an independent parameter. For a homogeneous central chain, we derive an integral expression for the thermal conductance $G$, which explicitly reveals its size-independent behavior in the thermodynamic limit. In this limit, the integral can be evaluated analytically in several cases: the classical limit with strong interfacial coupling, the classical limit with $\tau$ equal to the bond strength in the leads, and the weak interfacial coupling regime. Numerical simulations demonstrate that the theory developed for the thermodynamic limit remains accurate even for finite chains with as few as 100 atoms. The approach is further extended to estimate the size dependence of $G$ in chains with correlated mass disorder and weak, correlated bond disorder. These results show that the system-size scaling behavior of $G$ is insensitive to mass-spring correlations, impedance mismatch between the central chain and the leads, and interfacial coupling.

Graphons are measurable functions used to describe the asymptotic behavior of convergent graph families. Originally motivated by problems in combinatorics and graph theory, graphons have found numerous applications in the modeling and analysis of dynamical processes on networks. In this work, we use graphons to formulate the Ising model on convergent graph sequences, which include many network topologies common in applications. We derive the mean-field limit for the resulting model and obtain exact results for phase transitions in such systems. Specifically, we show that the critical temperatures of the Ising model on graphons are determined by the eigenvalues of the Hilbert–Schmidt operator associated with the graph limit. For many important network topologies, these eigenvalues can be computed explicitly. We illustrate our results with three representative random network models: Erdős–Rényi, small-world, and power-law. In the small-world case, we demonstrate phase transitions to both ferromagnetic and antiferromagnetic phases, as well as coexistence of local minima of the free energy. The latter gives rise to multistability, as confirmed by Monte-Carlo simulations. The results of this work demonstrate that the Ising model on graphons combines the analytical tractability of exactly solvable mean-field models with the ability to accommodate a broad range of network topologies. We expect that the use of graphons in spin models will lead to new insights into the statistical physics of interacting systems on complex networks.

We investigate the weakly nonlinear dynamics of the flutter instability of a planar Cosserat rod in a viscous fluid driven by a terminal follower force. Building on our previous linear stability analysis, we derive Stuart-Landau amplitude equations governing the emergence and saturation of oscillations near the Hopf bifurcation. The Landau coefficients are expressed in terms of the critical eigenmode, its adjoint, and quadratic correction fields arising from the asymptotic expansion. The reduced theory predicts the criticality of the Hopf bifurcations, the saturated oscillation amplitude, and the nonlinear frequency correction, in quantitative agreement with direct numerical simulations for representative material parameter regimes. Applying the theory to both stability boundaries of the finite oscillatory window, we find that the lower Hopf bifurcations are supercritical, whereas the upper restabilization threshold is subcritical. These results provide a normal-form description of follower-force-driven oscillations in geometrically exact Cosserat rods and a reduced framework for studying nonconservative elastohydrodynamic instabilities in soft robotic structures and active filaments.

We study the spread of defection in evolutionary games on networks using deterministic replicator dynamics posed on graphs. Each node hosts a mixed population of cooperators and defectors interacting through a Prisoner's Dilemma payoff matrix, with nearest-neighbor coupling determined by the network adjacency matrix. We develop two complementary analytical approximations that quantify how network architecture influences the timescale over which cooperation collapses. In a weak-coupling regime, internode interactions act as a small perturbation, yielding explicit approximate solutions on general graphs. For networks with strongly heterogeneous degree distributions, we derive a quasisteady approximation based on the natural separation of timescales between high- and low-degree nodes. Using these approximations, we introduce a defection spreading-time metric and show that the collapse of cooperation exhibits robust power-law scaling with system size across a broad range of network topologies. Analytical predictions are validated numerically on lattices, star graphs, incrementally connected graphs, small-world networks, and scale-free networks. The analysis shows that, to leading order, defection dynamics are controlled by local nodal degree, while network coupling and degree heterogeneity provide secondary corrections that influence the global collapse dynamics. We further show that increasing degree heterogeneity increases the average defection time, providing a complementary spectral interpretation through the principal eigenvalue of the adjacency matrix and related measures of graph irregularity. These results quantify how network architecture controls the transient dynamics of evolutionary collapse and establish new connections between evolutionary game dynamics and spreading processes on networks.

The coevolution of strategies and interactions is investigated with players located on a square lattice with interactions between first and second neighbors. The pair interactions are described by two-strategy (cooperation or defection) donation games with variable cost and benefit parameters for each player. During the evolutionary process, the players can adopt strategy or payoff parameters from one of their neighbors with a payoff-dependent probability. Numerical simulations indicate the formation of homogeneous defection or cooperation depending on the initial strategy and payoff distributions. The introduction of weak and rare mutations in the payoff adoption proves beneficial for the cooperative state, in which it increases the average payoff linearly in time. In contrast, the population cannot capitalize on the possibility of innovations in its defective state.

We investigate geometric percolation in two-dimensional assemblies of randomly positioned, widthless sticks of uniform length. The stick orientations are sampled from probability density functions with a vanishing mean orientational order parameter, while their higher-order structure varies continuously from perfect isotropy to perfect cross-alignment. Monte Carlo simulations show that the percolation threshold is lowest for the isotropic distribution and increases toward the perfectly cross-aligned limit. This variation is strongly nonuniform: small orientational perturbations near perfect cross-alignment produce substantially larger changes in the threshold than comparable perturbations near isotropy. The simulation results are interpreted using an orientation-resolved eigenvalue formulation based on the full excluded-area kernel and a fully preaveraged excluded-area approximation. For the probability density functions considered, the two formulations predict nearly identical thresholds. Orientation-dependent variations in the expected contact numbers therefore provide only a minor correction, whereas the dominant orientational dependence is retained by the averaged excluded area between pairs of sticks. A harmonic representation of this quantity further shows that the second moment captures the leading variation near isotropy, while progressively higher-order moments are required as the distribution approaches perfect cross-alignment. The results identify the orientational information that must be retained to predict geometric percolation in distributions having the same mean order parameter but different higher-order structures.

Distortions in the electron distribution function driven by intense temperature gradients critically influence the heat transport and the generation and evolution of magnetic fields in plasmas under the condition of inertial confinement fusion. Describing such kinetic behaviors at large spatiotemporal scales typically requires multigroup models based on simplified Vlasov-Fokker-Planck equations. However, the existing multigroup models cannot correctly describe the nonlocal effects in magnetized plasmas. This paper develops an improved nonlocal multigroup model for magnetized plasmas. The advancements include the following: (i) a revised source term in the diffusion equations, (ii) a Biermann-producing electric field incorporating the density perturbation, and (iii) a nonlocal correction method for the Nernst velocity. The numerical implementation is described and the stability of the anisotropic heat conduction equation is analyzed. Three test cases demonstrate that the model accurately predicts the key phenomena arising from nonlocal effects in magnetized plasmas.

Quantum many-body scars (QMBSs) in kinetically constrained systems provide a prominent example of weak ergodicity breaking beyond the eigenstate thermalization hypothesis (ETH). In this work we formulate an open-system perspective on constrained dynamics, where kinetic constraints are interpreted as a balance of information exchange between the system and an auxiliary environment. This viewpoint naturally introduces a quasiparticle number that characterizes the information balance and motivates a revised ETH for constrained systems. Specifically, the eigenstate expectation values of local observables can be approximated by a grand-canonical-like average defined on the energy–quasiparticle-number plane. For the off-diagonal part of local observables, the relevant density of states (DOS) is generalized to the same plane and controls the typical magnitude of off-diagonal matrix elements. The revised ETH accurately describes long-time averages and temporal fluctuations of local observables for both QMBSs and thermal dynamics. Within this framework, scarred dynamics arises from low-DOS regions on the energy–quasiparticle-number plane, where off-diagonal elements are less suppressed and the approximate spectrum-generating algebra becomes more pronounced. Our results provide a unified description of thermalization and QMBSs in kinetically constrained systems.

We derive a general relation between the velocity and force autocorrelation tensors (VACT and FACT) for a Brownian particle subject to an external magnetic field. Using time-symmetry arguments, we show that, for the full Langevin dynamics, the VACT depends only on the FACT, independently of the details of the interaction potential. Under the hypothesis of timescale separation between thermalization and interaction-driven motion, this relation simplifies considerably in the overdamped (Brownian) limit. A central feature of the overdamped result is that, unlike in the field-free case, the part of the VACT that controls the self-diffusion of the particle couples to the antisymmetric part of the FACT, with a coupling strength set by the ratio of the cyclotron frequency to the thermalization rate. We validate and illustrate the formalism on an exactly solvable model: a dimer of charged particles bound by a harmonic potential. Depending on the relative sign of the particle charges, the magnetic field is found to produce either a transient suppression of mobility and diffusion that is fully recovered at long times, or a persistent oscillatory force autocorrelation, regions of negative mobility, and a long-time suppression of self-diffusion.

We study the spectral stability of traveling and stationary front and pulse solutions in a class of degenerate reaction diffusion systems. We characterize the essential spectrum of the linearized operator in full generality and identify conditions under which it lies entirely in the left half plane. For a number of special cases, we obtain analytical results, including explicit Evans functions and complete spectral descriptions for certain stationary waves. In regimes where analytical methods are not available, we compute the point spectrum numerically using a Riccati–Evans function approach. Our results show that stable traveling fronts can occur, while traveling pulses are generically unstable.