Uhlenbeck and Ornstein presented their theory of a passive Brownian particle in a harmonic potential in 1930. Despite intensive research on active Brownian particles since the 1990s, a complete theory of their inertial motion in a confining force field has yet to be developed. Here, we present rigorous calculations of the steady-state position and velocity autocorrelation functions of an active (self-propelled) Brownian particle with translational and rotational inertia in a two-dimensional harmonic trap. Our results show that the well-known active Ornstein-Uhlenbeck particle inertial model can be used as an approximated treatment of the dynamics of a fully inertial active Brownian particle in a trap, but only within a relatively small range of system parameters. Beyond this range, rotational inertia significantly impacts particle dynamics. In particular, for sufficiently strong confinement, the theory predicts a new mode of active particle dynamics that differs radically from all known dynamical modes of trapped active and passive Brownian particles. In this case, rotational inertia suppresses the oscillatory behavior of the mean-square displacement evolution function, resulting in additional quasiballistic motion. We discuss possible experimental implementations of this dynamical mode.

We investigate the impact of random pinned disorder on a collection of self-propelled particles. To achieve this, we construct a continuum model by formulating the coupled hydrodynamic equations for slow variables: local density and momentum density of particles. The disorder in the system acts as pinning sites, effectively immobilizing the particles that come into contact with them. Our numerical results reveal that weak disorder leads to phase separation in the system at density and activity lower than the typical values for motility-induced phase separation. We construct a phase diagram using numerical simulations as well as linearized approximation in the plane of activity and packing fraction of particles at weak disorder densities. On increasing disorder density, the system shows the microphase separation, while at large disorder densities the system becomes heterogeneous and eventually undergoes kinetic arrest. The structure factor tail deviates from Porod's law, indicating increased roughness at domain interfaces under strong disorder. Furthermore, we analyze the fractal dimension of the interface as a function of disorder density, highlighting the increasing irregularity of phase-separated domains. We also find that disorder significantly suppresses number fluctuations in the system.

We investigate the percolation behavior of Fortuin-Kasteleyn-type clusters in the spin-$1/2$ Baxter-Wu model with three-spin interactions on a triangular lattice. The considered clusters are constructed by randomly freezing one of the three sublattices, resulting in effective pairwise interactions among the remaining spins. Using Monte Carlo simulations combined with a finite-size scaling analysis, we determine the percolation temperature of these stochastic clusters and show that it coincides with the exact thermal critical point of the model. The critical exponents derived from cluster observables are consistent with those of the underlying thermal phase transition. Finally, we analyze the dynamical scaling of the multicluster and single-cluster algorithms resulting from the cluster construction, highlighting their efficiency and scaling behavior with system size.

Most previous studies on stochastic resonance (SR) have focused on networks with pairwise interactions, neglecting the significant influence of higher-order interactions on collective behaviors. In this work, we investigate the SR of a coupled array of bistable oscillators with higher-order interactions. Our results show that higher-order interactions enhance both temporal SR and spatial synchronization among the oscillators. Although pairwise coupling can enhance SR, this enhancement diminishes once the pairwise coupling strength becomes excessively strong. We demonstrate that even under excessively strong higher-order coupling strength, higher-order interactions can continuously enhance SR within the parameter range we examined. The ability of higher-order interactions to provide sustained enhancement is attributed to the nonlinear components embedded in the higher-order coupling, which inhibit the oscillators from entering identical synchronization at large coupling strengths. We also find that the coupling radius has a noticeable influence on SR, where a larger radius generally produces stronger resonance. In addition, we identify a finite-size effect present in both pairwise and higher-order couplings, whereby the enhancement of SR is maximized when the network size is moderate, neither too large nor too small. Our results offer potential insights into the propagation of weak signals in higher-order networks.

Dense, microbial communities are shaped by local interactions between cells. Both the nature of interactions, spanning antagonistic to cooperative, and the strength of interactions vary between and across microbial species and strains. These local interactions can influence the emergence and maintenance of microbial diversity. However, it remains challenging to link features of local interactions with spatially mediated coexistence dynamics given the significant variation in the microscopic mechanisms involved in cell-to-cell feedback. Here, we explore how microbial interactions over a broad range of ecological contexts spanning antagonism to cooperation can enable coexistence as spatially explicit domains emerge. To do so, we introduce and analyze a family of stochastic coordination games, where individuals do better when playing (i.e., interacting) with individuals of the same type than when playing with individuals of a different type. Using this game-theoretic framework, we show that the population dynamics for coordination games is governed by a double-well shaped interaction potential. We find that in a spatial setting this double-well potential induces phase separation, facilitating coexistence. Moreover, we show that for microbes engaged in symmetric coordination games, phase separation takes on a universal scaling that follows “Model A” coarsening, consistent with prior experimental observations for Vibrio cholerae mutual killers. Finally, we derive a partial differential equation equivalent of the spatial stochastic game, confirming both the double-well nature of spatial coordination games and the universality of phase separation. Altogether, this work extends prior findings on the link between microbial interactions and population structure and suggests generic mechanisms embedded in local interactions that can enable coexistence.

We study the statistics of dynamical quantities associated with magnetic reconnection events embedded in a sea of strong background magnetohydrodynamic turbulence using direct numerical simulations. We focus on the relationship of the reconnection properties to the statistics of global turbulent fields. We show that the distribution in turbulence of reconnection rates (determined by upstream fields) is strongly correlated with the magnitude of the global turbulent magnetic field at the correlation scale. The average reconnection rates, and associated dissipation rates, during turbulence are thus much larger than predicted by using turbulent magnetic field fluctuation amplitudes at the dissipation or kinetic scales. Magnetic reconnection may, therefore, be playing a major role in energy dissipation in astrophysical and heliospheric turbulence.

We introduce a three-stroke quantum isochoric cycle that functions as a heat engine operating between two thermal reservoirs. Implemented for a particle confined in a one-dimensional infinite potential well, the cycle's performance is benchmarked against the classical three-stroke triangular and isochoric engines. We find that the quantum isochoric cycle achieves a higher efficiency than both classical counterparts and also surpasses the efficiency of the recently proposed three-stroke quantum isoenergetic cycle. Owing to its reduced number of strokes, the design substantially lowers control complexity in nanoscale thermodynamic devices, offering a more feasible route to experimental realization compared to conventional four-stroke architectures. We further evaluate the cycle in graphene-based systems under an external magnetic field, including monolayer graphene, AB-stacked bilayer graphene, and twisted bilayer graphene at both magic and nonmagic twist angles. Among these platforms, magic-angle twisted bilayer graphene attains the highest efficiency at fixed work output, highlighting its promise for quantum thermodynamic applications.

We analyze the structure and dynamics in the low-density phase of the deterministic two-dimensional cellular automaton model of traffic flow introduced in [O. Biham, A.A. Middleton, and D. Levine, Phys. Rev. A 46, R6124(R) (1992)]. The model consists of horizontally oriented (H) cars that move to the right and vertically oriented (V) cars that move downward, on a square lattice of size $L$ with periodic boundary conditions. Starting from a random initial state of density $p$, which is equally divided between the H- and V-cars, the model exhibits a phase transition at a critical density $p_c$. For $p<p_c$, it evolves toward a free-flowing periodic (FFP) state, while for $p>p_c$, it evolves toward a fully jammed state or to an intermediate state of congested traffic. In the FFP states, the H- and V-cars segregate into homogeneous diagonal bands, in which they move freely without obstruction. To analyze the convergence toward the FFP states, we introduce a configuration-space distance measure $D\left(t\right)=D_{\parallel }\left(t\right)+D_{\perp }\left(t\right)$ between the state of the system at time $t$ and the set of FFP states. The $D_{\parallel }\left(t\right)$ term accounts for the interactions between homotypic pairs of H- (or V-) cars, while $D_{\perp }\left(t\right)$ accounts for the interactions between heterotypic pairs of H- and V-cars. We show that in the FFP states $D\left(t\right)=0$, while in all the other states $D\left(t\right)>0$. As the system evolves toward the FFP states, there is a separation of timescales, where $D_{\parallel }\left(t\right)$ decays very fast, while $D_{\perp }\left(t\right)$ decays much more slowly. Moreover, the time dependence of $D_{\perp }\left(t\right)$ is well fitted by an exponentially truncated power-law decay of the form $D_{\perp }\left(t\right)\sim t^{-\gamma }exp(-t/{\tau }_{\perp })$, where ${\tau }_{\perp }$ depends on $L$ and $p$. The power-law decay suggests avalanche-like dynamics with no characteristic scale, while the exponential cutoff is imposed by the finite lattice size.

The shortest-path-percolation (SPP) model aims at describing the consumption and eventual exhaustion of a network's resources. Starting from a network containing a macroscopic connected component, random pairs of nodes are sequentially selected, and if the length of the shortest path connecting the node pairs is smaller than a tunable budget parameter, then all edges along such a path are removed from the network. As edges are progressively removed, the network eventually breaks into multiple microscopic components, undergoing a percolation-like transition. It is known that the SPP transition on Erdős-Rényi networks (ERNs) belongs to the same universality class as the ordinary bond percolation if the budget parameter is finite; for an unbounded budget, instead, the SPP transition becomes more abrupt than the ordinary percolation transition. By means of large-scale numerical simulations and finite-size scaling analysis, here we study the SPP transition on random scale-free networks (SFNs) characterized by power-law degree distributions. We find, in contrast with ordinary percolation, that the transition is identical to the one observed on ERNs, denoting independence from the degree exponent. Still, we distinguish finite- and infinite-budget SPP universality classes. Our findings follow from the fact that the SPP process drastically homogenizes the heterogeneous structure of SFNs before the SPP transition takes place.

Several power-law critical properties involving different statistics in natural languages—reminiscent of scaling properties of physical systems at or near phase transitions—have been documented for decades. The recent rise of large language models has added further evidence and excitement by providing intriguing similarities with notions in physics such as scaling laws and emergent abilities. However, specific instances of classes of generative language models that exhibit phase transitions, as understood by the statistical physics community, are lacking. In this work, inspired by the one-dimensional Potts model in statistical physics, we construct a simple probabilistic language model that falls under the class of context-sensitive grammars, which we call the context-sensitive random language model, and numerically demonstrate an unambiguous phase transition in the framework of a natural language model. We explicitly show that a precisely defined order parameter—that captures symbol frequency biases in the sentences generated by the language model—changes from strictly zero to a strictly nonzero value (in the infinite-length limit of sentences), implying a mathematical singularity arising when tuning the parameter of the stochastic language model we consider. Furthermore, we identify the phase transition as a variant of the Berezinskii–Kosterlitz–Thouless (BKT) transition, which is known to exhibit critical properties not only at the transition point but also in the entire phase. This finding leads to the possibility that critical properties in natural languages may not require careful fine-tuning nor self-organized criticality, but are generically explained by the underlying connection between language structures and the BKT phases. From a statistical physics perspective, our paper captures a rare phenomenon of the BKT phase in a one-dimensional system, as the BKT phase is widely studied and believed to exist only in two-dimensional systems.

Electroconvective flow near ion-selective surfaces is a fundamental phenomenon in electrochemistry that has attracted significant attention across disciplines such as membrane science, drug delivery, and ion transport. Despite this interest, a comprehensive understanding of electroconvective transport across the transition from weakly to strongly confined channels remains elusive. In this study, we investigate electroconvective transport in charged confined channels containing an embedded ion-selective membrane using direct numerical simulations. The Poisson-Nernst-Planck equations are modified to incorporate ionic steric effects. This work focuses on how variations in the steric parameter influence electroconvection across channels with varying degrees of confinement and electric double layer (EDL) overlap, while maintaining a fixed electrohydrodynamic coupling parameter. Under strong confinement, where EDLs overlap, electroconvective transport is primarily governed by steric effects. In this regime, the average ion concentration exhibits an inverse relationship with the steric parameter. In contrast, under weak confinement—where EDLs do not overlap—electroconvective flow dominates the transport mechanism. Here, a decrease in the dimensionless Debye number leads to an increase in the velocity of electroconvective vortices. Above a critical dimensionless Debye number, the transition in transport mechanism—from electroconvective flow to steric (ion size) effects—can be captured through an asymptotic scaling law involving both the dimensionless Debye number and the dimensionless steric parameter. These results establish a framework that connects the behavior of electroconvective transport in weakly and strongly confined channels.

By tailoring the target density to a radial gradient distribution, we propose a proton focusing mechanism. This mechanism is based on the focusing radial electric field self-induced by the radial density gradient. This field, different from the defocusing field of a uniform density target, focuses near the longitudinal axis of the target and is capable of producing a proton source with a nanometer-scale focal spot size, and an emittance on the order of ${10}^{-3}\mathrm{mm}\mathrm{mrad}$. This type of proton source offers further improvements in both focal spot size and collimation over other proton focusing enhancement mechanisms.

Nonlinear elements in a rectifying circuit can be used to harvest energy from thermal fluctuations either steadily or transitorily. We study an energy-harvesting system comprising a small variable capacitor (e.g., freestanding graphene) wired to two diodes and two storage capacitors that may be kept at different temperatures (or at a single one) and use two current loops. The system reaches very rapidly a quasistationary state with constant overall charge while the difference of the charges at the storage capacitors evolves much more slowly to its stationary value. In this paper we extract an exponentially small factor out of the solution of the Fokker-Planck equation and use a Chapman-Enskog procedure to describe the long evolution of the marginal probability density for the charge difference, from the quasistationary state to the final stationary state (thermal equilibrium for equal temperatures). The following paper [J. M. Mangum et al., Phys. Rev. E 113, 014124 (2026)] shows that the results of the perturbation procedure compare well with direct numerical simulations. For a specific form of the diodes' nonlinear mobilities, we can approximate the quasistationary state by Gaussian functions and further study the evolution of the marginal probability density. The latter adopts the shape of a slowly expanding pulse (comprising left- and right-moving wave fronts whose fore edges become sharper as time elapses) in the space of charge differences that leaves the final stationary state behind it.

This study is presented in a series of two papers. The preceding paper [L. L. Bonilla et al., Phys. Rev. E 113, 014123 (2026)] is an analytical study. In the present paper we numerically study the thermal energy-harvesting capability of two electronic circuits. The first circuit consists of a diode and capacitor in series. We solve the time-dependent Fokker-Planck equation and show that the capacitor initially charges and then discharges to zero. The peak charge on the capacitor increases with temperature, capacitance, and diode quality. The second circuit has two current loops with one small capacitor, two storage capacitors, and two diodes wired in opposition. When the diodes are held at different temperatures we observe that a nonzero steady-state charge is accumulated on both storage capacitors. The magnitudes of the stored charges are nearly equal, but the signs are opposite. When resistors are used in place of diodes there is no transient and no steady-state charge buildup. Numerical studies for the time-independent Fokker-Planck equation are presented and confirm the steady-state charges.

A generalized telegrapher equation associated with intermittent changes in the sign velocity of Kac's flights has been studied in the presence of the resetting mechanism. To solve this problem, we used the fluctuation-dissipation theorem to write a memorylike master equation approach to obtain the solution for the evolution of a normalized positive distribution. This distribution is associated with an intermittent hyperbolic diffusionlike process. We studied the time-dependent propagator and its stationary distribution. The variance for the evolution of the profile has been studied as a function of the resetting time. An approach is presented to tackle the problem of the mean first passage time for the intermittent telegrapher equation with resetting. The limiting cases of ordinary diffusion and ordinary telegrapher equations with resetting are also studied.

Quantum dynamics of the Harper model with self-duality exhibits localized, diffusive, and ballistic states depending on the potential strength $V$. By adding time-dependent harmonic perturbations composed of $M$ incommensurate frequencies, we show that all states of the Harper model transition to quantum diffusive states as the perturbation strength $\epsilon$ increases for $M\ge 3$. The transition schemes and diffusion behaviors are discussed in detail and the phase diagram in the $(\epsilon ,V)$ parameter space is presented.