We theoretically explore the dynamics of a chiral active Ornstein-Uhlenbeck particle confined in a two-dimensional anisotropic harmonic trap. The particle is driven by chirality and is coupled to two orthogonal heat baths, potentially at two different temperatures. Using both analytical approach and numerical simulation, we explore the rotational dynamics of the particle in both viscous and viscoelastic environments. While the particle is suspended in a viscoelastic bath, characterized by a finite memory timescale, we interestingly observe that even in the absence of a temperature gradient, the angular momentum changes its sign as a function of the memory timescale, reflecting the direction reversal of rotational motion of the particle, and it is solely due to the interplay between memory and chirality. This direction reversal is a distinct memory-induced phenomenon and does not occur in the viscous limit. Moreover, increasing (or decreasing) the temperature gradient shifts the magnitude of the angular momentum further into the negative (or positive) direction, selecting a unique direction of rotation for the particle throughout the activity-memory parameter space. However, in the viscous limit, the direction reversal of the rotational motion is still possible but occurs only across a neutral line in parameter space, along which the contributions from both chirality and thermal anisotropy to the net angular momentum exactly cancel. These results highlight a distinct mechanism for directional control in active systems, with memory enabling reversal phenomena unique to viscoelastic media.

In a recent work [Phys. Rev. E 109, L042102 (2024)], interesting dimensional crossovers [from two- to one-dimensional (2D to 1D) scaling] were found in the growth of Kardar-Parisi-Zhang (KPZ) interfaces on rectangular substrates, with lateral sizes $L_y>L_x$. Here, we extend this study to other universality classes for interface growth—specifically, the Edwards-Wilkinson (EW), the Mullins-Herring (MH), and the Villain-Lai-Das Sarma (VLDS) classes. From extensive simulations, we demonstrate that, in all systems with sufficiently large aspect ratio $\mathcal{R}=L_y/L_x$, the roughness $W$ scales with time $t$ in the growth regime as $W\sim t^{{\beta }_{\text{2D}}}$ for $t\ll t_c$ and $W\sim t^{{\beta }_{\text{1D}}}$ for $t\gg t_c$, where $t_c\sim L_x^{z_{2\text{D}}}$ in most cases. For the VLDS class, this crossover is also observed in the height distribution (HD), which approaches its characteristic probability density function for the 2D case at short times ($t\ll t_c$) and then crosses over to the asymptotic 1D HD. Dimensional crossovers are also found in the steady-state regime, both in the roughness scaling and in the VLDS HD, which interpolate between the 2D and 1D ones as $\mathcal{R}$ increases. The particular case $L_x=L_y^{\delta }$, with $0<\delta <1$, is also discussed in detail and reveals interesting features of the investigated systems. For instance, there exists a “special” exponent ${\delta }^{*}=z_{1\text{D}}/z_{2\text{D}}$ such that the temporal crossover cannot be observed for $\delta >{\delta }^{*}$. Moreover, this leads the saturation roughness to display a nonuniversal scaling, $W_s\sim L_y^{\mathrm{\Lambda }}$, with $\mathrm{\Lambda }=(1-\delta ){\alpha }_{1\text{D}}+\delta {\alpha }_{2\text{D}}$.

We investigate a class of models of high-dimensional dynamics with all-to-all, random, and nonreciprocal interactions. We determine the dynamical phase diagram and show the emergence of chaotic dynamics. Correspondingly, we show that the dynamical equations exhibit a number of equilibria that is exponentially large in the system's dimensionality, all linearly unstable in the chaotic phases. Solving the effective equations governing the dynamics in the infinite-dimensional limit, we determine the typical properties (magnetization, overlap) of the configurations belonging to the attractor manifold. We show that these properties cannot be inferred from those of the equilibria, challenging the expectation that chaos can be understood purely in terms of the numerous unstable equilibria of the dynamical equations. We discuss the dependence of this scenario on the strength of nonreciprocity. The results are obtained combining analytical methods such as dynamical mean-field theory and the Kac-Rice formalism.

We consider a microscopic model of an inhomogeneous environment where an arbitrary quantum system is locally coupled to a harmonic bath via a finite-range interaction. We show that in the overdamped regime the position distribution obeys a classical Kramers-Moyal equation that involves an infinite number of higher-order derivatives, implying that the finite bath correlation length leads to non-Gaussian Markovian noise. We analytically solve the equation for a harmonically bound particle and analyze its non-Gaussian diffusion as well as its steady-state properties.

We investigate coherent quantum transport on multilayer complex networks composed of treelike scale-free layers. The general principles governing transport efficiency are uncovered under continuous-time quantum walks by tuning the degree distribution exponent $\gamma$, which interpolates between starlike and chainlike structures, and the interlink probability $q$. We show that global transport efficiency improves with increasing $\gamma$, increasing the number of layers, and increasing interlayer connectivity. The symmetry breaking and the decrease of spectral degeneracy of Laplacian maximally enhance transport efficiency when exactly one interlink between any pair of adjacent layers is removed. Notably, due to reduced structural symmetries nonidentical layers yield better transport than identical ones.

The formulation of a fluctuating hydrodynamic theory for interacting particles is a crucial step in the theoretical description of liquids. The microscopic mappings proposed decades ago by Dean and Kawasaki have played a central role in the analytical treatment of such problems. However, the singular mathematical nature of the density distributions used in these derivations raises concerns about the validity and practical utility of the resulting stochastic partial differential equations, particularly for direct numerical simulations. Recent efforts have centered on establishing a rigorous coarse-graining procedure to regularize the effective Dean-Kawasaki equation. Building on this foundation, we numerically investigate weakly interacting fluids within such a regularized framework. Our work reveals, at the level of structural correlations, the effects of regularization on the Dean-Kawasaki formalism and paves the way for improved numerical approaches to simulate fluctuating hydrodynamics in liquids.

In this paper, we investigate Turing instability in a diffusive predator-prey system with an opportunistic predator and a weak Allee effect in the prey population. We begin by applying the upper-lower solution method to establish the existence of positive solutions and to derive estimates for both the positive and steady-state solutions. We then show that diffusion can trigger Turing instability in the homogeneous steady states of the system. Numerical simulations are carried out to support the analytical results. In particular, we further examine a stochastic reaction–diffusion version of the model by introducing additive white noise. A comparison between the stochastic and deterministic cases reveals that white noise can enhance the stability of the system.

Simplified stochastic models are widely used in the study of frequency-resolved noise propagation in biochemical reaction networks, a common measure being the coherence between random fluctuations in molecule number trajectories. Such models have also found widespread application in the quantification of how information is transmitted in reaction networks via the mutual information (MI) rate. A common assumption is that under timescale separation, estimates for the coherence and MI rate obtained from simplified (reduced) models closely approximate those in the underlying full models. Here, we challenge that assumption by showing that while reduced models can faithfully reproduce low-order statistics of molecular counts, they frequently incur substantial discrepancies in the coherence spectrum, especially at intermediate and high frequencies. These errors, in turn, lead to significant inaccuracies in the resulting estimates for the MI rates. We show that the observed discrepancies are due to the interplay between the structure of the underlying reaction networks, the specific model reduction method that is applied, and the asymptotic limits relating the full and reduced models. We illustrate our results in canonical models of enzyme catalysis and gene expression, highlighting practical implications for quantifying information flow in cells.

The optimization of the conversion of thermal energy into work and the minimization of dissipation for nano- and mesoscopic systems is a complex challenge because of the important role fluctuations play on the dynamics of small systems. I generalize the work of Esposito et al. [Europhys. Lett. 89, 20003 (2010)] to optimize at all driving speeds the control needed to extract the maximum amount of work from any effective two-level systems. These emerge when one coarse grains degrees of freedom, which is often unavoidable to obtain “real-world” two-level systems. In particular, I allow even for the system to have underlying quantum dynamics, as long as these allow for a coarse graining that leads to a Markovian master equation. I analyze the finite-time thermodynamics of these systems and find the thermodynamically optimal protocols, which depend on the size of the coarse graining needed to obtain a two-level system. Furthermore, I use these results to derive speed limits for any transformation performed on an effective two-level system.

The manipulation of mass diffusion is crucial for applications spanning biotechnology to chemical engineering. However, established methods for designing diffusion metadevices are often constrained by high background diffusivity, inherent anisotropy, or implementation complexity. Here we present a unified theoretical framework for isotropic mass diffusion control that bridges transformation optics and convective transport. By applying homogenization theory to established convection-enhanced diffusion mechanisms, we demonstrate that a rotating fluid core effectively emulates the behavior of a near-zero-index medium in optics and thermotics. By combining this effective description with pseudoconformal mapping, we design an isotropic concentration cloak that remains applicable even in high-diffusivity environments. Numerical simulations validate that the cloak maintains robust performance for arbitrary target shapes in high-diffusivity regimes. Notably, the cloaked region remains sensitive to the external environment, allowing the internal concentration to track background changes in real time. A feasible experimental suggestion using perforated structures is also proposed. This work provides a diffusion-based reinterpretation of near-zero-index-inspired concepts and a synthesis of fluid mechanics and pseudoconformal mapping, offering a unified and practically accessible framework for engineering diffusive fields.

Driven nonequilibrium lattice models have wide-ranging applications in contexts such as mass transport, traffic flow, and transport in biological systems. In this work, we investigate the steady-state properties of a one-dimensional lattice system that allows multiple particle occupancy on each site. The particles undergo stochastic nearest-neighbor jumps influenced by both a directional bias and on-site repulsive interactions of the Bose-Hubbard type. With periodic boundary conditions, we observe a nonmonotonic dependence of intersite correlation functions on the interaction strength. At large interaction strengths, the state consists of quiescent stacks of stationary particles along with an emergent asymmetric simple exclusion process, and the particle current exhibits a periodic dependence on density. In contrast, with open boundary conditions, the system displays steplike density profiles reminiscent of those in tilted Bose-Hubbard systems, and a regime with a macroscopic number of empty sites followed by a steep parameter-dependent increase in density. Our results highlight how the interplay between drive, interaction, and boundary conditions leads to distinctive signatures on the current and density profiles in the steady state in different regimes.

We study stochastic transport of interacting particles on a disordered network described by the random comb geometry. The model is defined on a one-dimensional backbone from which branches of random lengths emanate, providing a minimal model of percolation networks beyond the critical percolation probability. The dynamics obeys local detailed balance with respect to a Bose-Hubbard Hamiltonian containing both an external bias and on-site repulsion. This choice yields an analytically tractable steady state through a mapping to the zero-range process. We compute the backbone current, branch density profiles, and macroscopic drift velocity, and analyze how bias and interactions compete to shape transport. The backbone current increases monotonically with density, while the drift velocity displays a nonmonotonic dependence on the external field, remaining finite for any nonzero bias, in contrast to the vanishing drift velocity of noninteracting particles beyond a threshold bias. Density profiles along branches exhibit stepwise plateaus governed by the ratio of interaction to bias energy. These results highlight how repulsive interactions suppress trapping and restore transport in disordered geometries, bridging earlier studies of field-induced drift in random networks with the physics of disordered Bose-Hubbard systems.

We study the aspects of quantum chaos in mushroom billiards introduced by Bunimovich. This family of billiards classically has the property of mixed phase space with precisely one entirely regular and one fully chaotic (ergodic) component, whose size depends on the width $w$ of the stem, and has two limiting geometries, namely the circle (as the integrable system) and stadium (as the fully chaotic system). Therefore, this one-parameter system is ideal to study the semiclassical behavior of the quantum counterpart. Here, in paper I, we study the spectral statistics as a function of the geometry defined by $w$ and as a function of the semiclassical parameter $k$, which in this case is just the wave number $k$. We show that at sufficiently large $k$ the level spacing distribution is excellently described by the Berry-Robnik distribution (without fitting). At lower $k$ the small deviations from it can be well described by the Berry-Robnik-Brody distribution, which captures the effects of weak dynamical localization of Poincaré-Husimi functions. We also employ the analytical theory of the level spacing ratios distribution $P\left(r\right)$ for mixed-type systems, recently obtained by Yan [Phys. Rev. E 111, 054213 (2025)], which does not require a spectral unfolding procedure, and show excellent agreement with numerics in the semiclassical limit of large $k$. In paper II [M. Orel and M. Robnik, Phys. Rev. E 113, 044218 (2026)] we shall analyze the eigenstates by means of Poincaré-Husimi functions.

We investigate eigenstate localization in the phase space of the Bunimovich mushroom billiard, a paradigmatic mixed–phase–space system whose $\mathrm{piecewise}{C}^1$ boundary yields a single clean separatrix between one regular and one chaotic region. By varying the stem half-width $w$, we continuously change the strength and extent of bouncing-ball stickiness in the stem, which for narrow stems gives rise to phase space localization of chaotic eigenstates. Using the Poincaré–Husimi (PH) representation of eigenstates, we quantify localization via information entropies and inverse participation ratios of PH functions. For sufficiently wide stems, the distribution of entropy localization measures converges to a two-parameter beta distribution, while entropy localization measures and inverse participation ratios across the chaotic ensemble exhibit an approximately linear relationship. Finally, the fraction of mixed (neither purely regular nor fully chaotic) eigenstates decays as a power-law in the effective semiclassical parameter, in precise agreement with the principle of uniform semiclassical condensation of Wigner functions [H.-J. Stöckmann (1999); F. Haake (2010)].

In recent years, significant progress has been made in Fokker-Planck (FP) approximations of the Boltzmann equation, where binary collisions are modeled as drift and diffusion processes in velocity space. To address the discrepancy in the Prandtl number for the original linear FP model, several modified formulations have been developed. Among these, one strategy introduces additional degrees of freedom into the drift term. However, this leads to an increase in model complexity, as the presence of higher-order velocity moments complicates the solution of the equations with underdetermined parameters. An alternative strategy primarily modifies the diffusion term, but the anisotropy introduced in the diffusion term may compromise its positive definiteness. In this work, a quadratic-FP (quad-FP) model with correct Prandtl number is proposed. In the quad-FP model, a quadratic nonlinear modification is introduced into the drift term and corresponding anisotropy modifications are also implemented in the diffusion term. This design simplifies the model structure and facilitates numerical implementation. Moreover, it mitigates the anisotropy introduced by diffusion-term modification, better preserving the positive definiteness of the diffusion term even under strongly nonequilibrium conditions. Numerical tests demonstrate that the quad-FP model provides predictions consistent with direct simulation Monte Carlo results in a variety of flows and achieves improved computational efficiency.

We comment on the recent work by Yamaguchi and Barré [Phys. Rev. E 107, 054203 (2023)], which uses a linear stability analysis of the Vlasov equation to characterize phase transitions in a generalized Hamiltonian mean field model. By performing extensive molecular dynamics simulations with $N={10}^8$ particles, we demonstrate that the bifurcation analysis of the initial stationary distribution is insufficient to predict either the location or the nature of the phase transition to a quasi-stationary state (qSS). Specifically, we show that for bimodal momentum distributions, the instability threshold identified by the authors does not correspond to a ferromagnetic transition; instead, the system remains in a paramagnetic state characterized by magnetization oscillations with a zero time-average. We find that the true paramagnetic-ferromagnetic transition is discontinuous (first-order) and occurs at significantly larger coupling strengths. These results indicate that the linear stability analysis, in general, is not sufficient to predict symmetry-breaking phase transitions in long-range interacting systems.