Disks of two sizes are confined to a long and narrow channel. The axis and the plane of the channel are horizontal. The channel is closed off by pistons that freeze jammed microstates out of loose disk configurations, agitated randomly at calibrated intensity and subject to moderate pressure. Disk sizes and channel width are such that under jamming no disks remain loose and all disks touch one wall. The protocol permits disks to move past each other prior to jamming, which facilitates randomness in the sequence of large and small disks. We present exact results for the characterization of jammed macrostates including volume and entropy for given fractions of small and large disks as functions of energy parameters which depend on the jamming protocol. Our analysis divides the disk sequence of jammed microstates into overlapping tiles out of which we construct 17 species of statistically interacting quasiparticles. Jammed macrostates then depend on the fractions of small and large disks and on a dimensionless control parameter inferred from measures for expansion work against the pistons and intensity of random agitations. Two models are introduced for comparison of key technical aspects: one model emphasizes symmetry and the other mechanical stability. We distinguish regimes for the energy parameters that either enhance or suppress mixing of disk sizes in jammed macrostates. The latter case, if realizable, is a manifestation of grain segregation driven by steric forces alone, without directional bias.

High-quality quantum oscillators are preferred for precision sensing of external physical parameters because if the noise level due to interactions with the environment is too high, metrological information can be lost due to quantum decoherence. On the other hand, stronger interactions with a thermal environment could be seen as a resource for new types of metrological schemes. We present a general amplification strategy that enables the detection of zero-point fluctuations using low-quality quantum oscillators at finite temperature. We show that by injecting a controllable level of multiplicative frequency noise in a Brownian oscillator, quantum deviations from the virial theorem can be amplified by a parameter proportional to the strength of the frequency noise at constant temperature. As an application, we suggest a scheme in which the virial ratio is used as a witness of the quantum fluctuations of an unknown thermal bath, either by measuring the oscillator energy or the heat current flowing into an ancilla bath. Our work expands the metrological capacity of low-quality oscillators and can enable new measurements of the quantum properties of thermal environments by sensing their zero-point contributions to system variables.

Optomechanical cavities, with nonlinear photon-phonon interactions, offer a more compact approach to chaos generation than conventional feedback-based optical systems. However, proper study on chaos synchronization of two optomechanical cavities connected by optical means is still unexplored. In this work, we theoretically investigate all-optical complete synchronization between unidirectionally coupled optomechanical cavities in the master-slave configuration. Traditionally, achieving complete synchronization in nonlinear coupled oscillators and in optical systems necessitates identical systems. Our findings, which arise naturally from the fundamental mathematical properties of optomechanical cavities, demonstrate that parameter heterogeneity can, in fact, not only enable complete synchronization but make it stable.

We use a robust methodology that enables us to detect synchronous regions in networks of coupled dynamical systems and identify their collective behaviors. Our method employs ordinal patterns of spatial configuration of neighbor oscillators at each time point to ascertain whether or not neighboring nodes in a network are synchronized. We then use permutation entropy and forbidden sequence cardinality to classify collective behavior. We first demonstrate the effectiveness of our method on a time series of coupled identical logistic maps that are located on a ring. Our method not only confirms previous findings of collective behavior identification but also shows the borders of synchronous regions when oscillators of a network are partially synchronized. Then we apply our findings to a network of logistic maps with random connections to demonstrate the method's efficacy in situations where the network's spatiotemporal plots are not feasible.

In the field of quantum thermodynamics, optimizing the performance of quantum battery (QB) under environmental effects remains a primary research interest. However, environmental control remains challenging due to its high-dimensional degrees of freedom, particularly in the non-Markovian regimes. This work investigates the charging dynamics of a QB model subjected to a tunable non-Markovian environment. We show that a controllable non-Markovian setting can be exploited to improve the QB's primary figure of merit. Specifically, we show that by tuning the relative ratio of QB-charger coupling strength and charger-bath coupling strength, the maximum dynamic values of the charging power, energy storage, and work extraction of QB can be significantly increased. Our findings suggest that employing non-Markovian effects in a tunable way offers a promising avenue for enhancing the performance of quantum thermodynamic devices, and sheds new light on the intersection between the reservior engneering and quantum thermodynamics.

A universal and rigorous ensemble framework for nonequilibrium systems remains lacking. Here, we provide a concise framework for the generalized ensemble theory of nonequilibrium discrete systems using a matrix-based approach. By introducing an observation matrix, we show that any discrete probability distribution can be formulated as a generalized Boltzmann distribution, with observables and their conjugate variables serving as basis vectors and coordinates in a vector space. Within this framework, we identify the minimal sufficient statistics required to infer the Boltzmann distribution. The nonequilibrium thermodynamic relations and fluctuation-dissipation relations naturally emerge from this framework. Our findings provide a new approach to developing generalized ensemble theory for nonequilibrium discrete systems.

In recent years, unconventional computing architectures that transcend traditional semiconductor-based systems have witnessed far-ranging research interest. Here we propose an approach to the construction of logic gates, using active particles, specifically 1-pentanol-infused disks, exploiting the principle of the Marangoni effect. In our experimental setup, we design a channel with arms designated for inputs and an arm to observe the output. The inputs are provided by disks, where active disks infused with pentanol are considered to have a truth value of 1, while passive disks are considered to have a truth value of 0. The movement of a controller disk placed in a decision-making region determines the output. We demonstrate that the complex interplay of surface tension, drag, and repulsive and attractive forces yields the fundamental AND and OR logic responses. Interestingly, the logic function can be switched by solely changing the activity of the controller by decreasing the pentanol concentration, thus giving the same channels the capacity to morph the logic functionality. Additionally, the complementary NAND and NOR logic can be obtained with a simple change in the output encoding. Such active-matter-based logic gates have the potential to perform in fluid conditions, making them ideal for biomedical applications, bio sensing, molecular computing, and targeted drug delivery by responding to biological signals without external power sources.

A variety of bacterial species are able to spontaneously assemble into an aerotactic band, a local accumulation at a fixed distance from the air-water interface. Although the phenomenon is long known, its modeling so far is limited to mesoscopic, one-dimensional or numerical descriptions. We investigate band properties at the microscopic scale using exact solutions to the Fokker-Planck equation. First, we show that the interplay between oxygen consumption and tumbling modulation is governed by a third-order nonlinear differential equation relating the oxygen concentration to the aerotactic response. For two model aerotactic behaviors, we present analytical solutions and discuss the resulting band structure. Second, we investigate how an aerotactic band of magnetotactic bacteria in a magnetic field induces a fluid flow, as observed in experiments [Marmol et al., Phys. Rev. Lett. (2025), doi: 10.1103/qrgn-m91t]. In the low-field limit, we determine the bacterial distribution and the active stress tensor. Using the Green function of the hydrodynamic problem, we obtain a prediction for the fluid flow that is both simple and consistent with observations. Altogether, our results provide a model system of aerotactic band and solid ground for analyzing aerotaxis-driven self-organization.

We analyze the sedimentation behavior of a polydisperse two-dimensional liquid-crystal fluid using a local density-functional theory based on scaled particle theory. Polydispersity is incorporated through variations in the roundness of hard rectangular particles interacting solely via excluded area effects. Despite its simplicity, the model displays a rich phenomenology. In bulk, the fluid exhibits isotropic, nematic, and tetratic phases. In sedimentation, we obtain complex phase stacking diagrams featuring multiphasic stacking sequences with up to four stacks of different bulk phases, inverted stacking sequences such as top isotropic and bottom nematic together with top nematic and bottom isotopic, as well as stacking sequences with reentrant stacks such as tetratic and nematic stacks floating between two isotropic stacks. This phenomenology arises as a result of an intricate coupling between particle polydispersity and the effect of gravity. Our approach can be easily adapted to investigate the sedimentation behavior of other polydisperse colloidal systems.

Self-organized Turing patterns, arising from the dynamic interplay of reaction and diffusion processes, are instrumental in modeling natural morphogenesis and deciphering the biological functions of diverse structures. These patterns exhibit complex spatial arrangements that can be analyzed through the lens of statistical mechanics, particularly in relation to hyperuniformity—a state characterized by suppressed long-range density fluctuations. Despite this, the connection between Turing patterns and hyperuniformity remains relatively unexplored. In this study, we examine the spatial distribution of generic Gray-Scott patterns and Arabidopsis thaliana trichome patterns, linking their morphogenesis to disordered hyperuniform patterns. Our findings demonstrate that hyperuniformity emerges in Turing patterns as a solution to a reaction-diffusion equation system, reaching its apex in a specific region of the Gray-Scott phase space marked by dotlike spatial patterns. Mapping the hyperuniformity classes in this region reveals patterns with class III hyperuniformity surrounding special class I solutions. By extending this framework to biological systems currently under investigation for mechanosignalling triggrered immunity, we show that A. thaliana trichomes form class III disordered hyperuniform systems. Such exotic organization, as described by Turing patterning, has a strong potential to influence mechanically triggered immune response, offering novel insights into plant mechanoperception.

We study the interplay between critical isotropic elasticity and classical Ising criticality using a functional renormalization group (FRG) approach which is implemented such that the volume is fixed during the entire renormalization group flow. For dimensions slightly smaller than four, we use a simple truncation of the FRG flow equations to recover the fixed points of the constrained Ising model: the Gaussian fixed point G, the Ising fixed point I, the renormalized Ising fixed point R, and the spherical fixed point S. We show that the fixed points R and S are both characterized by a finite anomalous dimension $y_{*}<0$ of strain fluctuations, implying that the energy dispersion of longitudinal acoustic phonons exhibits a nonanalytic momentum dependence proportional to $k^{1-y_{*}/2}$ for small momentum $k$. We also derive and solve flow equations for the free energy at constant strain and compute stress-strain relations in the vicinity of the fixed points. As a result, we reaffirm that Ising criticality, controlled by the fixed point I, is preempted by a bulk instability. Beyond that, we find that the stress-strain relation at R and S remains linear to leading order (Hooke's law), as long as the interaction between strain and Ising fluctuations is sufficiently weak. However, the finite anomalous dimension of strain fluctuations $y_{*}$ gives rise to nonanalytic corrections to Hooke's law.

Building upon the framework established in our recent work [M. Seifi et al., Phys. Rev. E 111, 054114 (2025)], wherein a generalized Maxwell-Boltzmann distribution was formulated using the Mittag-Leffler function within the superstatistical formalism, we extend this approach to the quantum domain. Specifically, we introduce two statistical distributions—termed the Mittag-Leffler-Bose-Einstein (MLBE) and Mittag-Leffler-Fermi-Dirac (MLFD) distributions—constructed by generalizing the conventional Bose-Einstein and Fermi-Dirac distributions through the Mittag-Leffler function. This generalization incorporates a deformation parameter $\alpha$, which facilitates a continuous interpolation between bosonic and fermionic statistics, while inherently capturing nonequilibrium effects and generalized thermodynamic behavior. We analyze the thermodynamic geometry associated with these distributions and identify significant departures from standard statistical models. Notably, the MLBE distribution manifests a Bose-Einstein-like condensation even in the absence of interactions, whereas the MLFD distribution exhibits unconventional features, such as negative heat capacity in the low-temperature regime. These findings highlight the pivotal role of statistical deformation in determining emergent macroscopic thermodynamic phenomena.

Understanding how systems respond to external perturbations is a fundamental challenge in physics, particularly for nonequilibrium and nonstationary processes. The fluctuation-dissipation theorem provides a complete framework for near-equilibrium systems and various bounds have recently been reported for specific nonequilibrium regimes. Here, we present a compact, trajectory-score-based formulation that synthesizes and generalizes linear fluctuation-response relations for arbitrary Markov processes, decomposing system response into spatial correlations of local dynamical events. This decomposition reveals that response properties are encoded in correlations between transitions and dwelling times across the network, providing a natural generalization of the fluctuation-dissipation theorem and recently developed nonequilibrium linear response relations. Our theory unifies existing response bounds, extends them to time-dependent processes, and reveals fundamental monotonicity properties of the tightness of multiparameter response inequalities. Beyond its theoretical significance, this framework enables efficient numerical evaluation of response properties from sampling unperturbed trajectories, offering significant advantages over traditional finite-difference approaches for estimating response properties of complex networks and biological systems far from equilibrium.

We endow the elements of a random matrix drawn from the Gaussian unitary ensemble with a Dyson Brownian motion dynamics. We initialize the dynamics of the eigenvalues with all of them lumped at the origin, but one outlier. We solve the dynamics exactly, which gives us a window on the dynamical scaling behavior at and around the Baik-Ben Arous-Péché transition. Amusingly, while the statics is well known and accessible via the Hikami-Brézin integrals, our approach for the dynamics is explicitly based on the use of orthogonal polynomials.

We introduce and analyze a class of heat engines composed of interacting units, in which the thermal reservoir is associated with the neighborhood surrounding each unit. These systems can be mapped onto stochastic opinion models and are characterized by collective behavior at low temperatures, displaying different types of phase transitions, marked by spontaneous symmetry breaking and classifications that depend on topology, the neighborhood, and other ingredients. For the case of contact with two thermal baths—equivalent to each unit having $k=4$ nearest neighbors—the system can be tuned to operate at maximum power without sacrificing the efficiency $\eta$ and/or increasing dissipation $\overline{\sigma }$. All of them are related by a general expression when the worksource stems from different interaction energies. The heat engine placed in contact with more than three reservoirs is more revealing, showing that the intermediate thermal reservoir can be conveniently adjusted to achieve the desired compromise between power $\mathcal{P}$, efficiency, and dissipation. The influence of lattice topology (regular and random-regular networks), its relationship with collective operation, and distinct ratios between the temperatures of the thermal baths, has also been investigated.

In contrast to the central pattern generator hypothesis, which posits that neural networks generate rhythmic motor patterns without sensory feedback, recent robotics studies have demonstrated that independent oscillating agents with load-dependent feedback can organize coordinated gaits in quadrupedal robots. In this study, we develop minimal mathematical models to describe how such coordination emerges from physical interactions through the trunk and environment. By employing active rotators as limb controllers, we demonstrate their capacity to generate distinct gait patterns, including the trot, pace, and bound. We can also predict gait transitions with walking speed. These models provide insight into why different animals with specific physiques have limited gait patterns and offer suggestions for designing quadrupedal robots.

Coherently coupled nonlinear Schrödinger equations arise for wave interactions in media where the relative phase of the components is critical. An example is the propagation of electric fields in an optical waveguide in the weak birefringence limit. The competing factors are second-order dispersion and four-wave mixing. Doubly periodic structures of the nonlinear Schrödinger equation returning to their initial states after complex evolution have been previously studied. Recurrence for a coherently coupled system is studied here via approaches of spectral and linear instabilities. A doubly periodic solution for coherently coupled systems is established in terms of Jacobi elliptic functions, and its robustness is investigated. For spectral instability, the eigenvalues of the associated matrix are computed. For linear instability, direct numerical simulations are performed for slightly perturbed doubly periodic patterns. These patterns generally display various degrees of instability. Special disturbances favorable for recurrence phenomena arising from a continuous wave background and singly periodic solutions are identified. The agreement between spectral and linear instabilities on the trends of growth of disturbances is excellent. Knowledge gained here will be useful for studying wave evolution and instabilities in fluids and optics.

A type of chaos called laminar chaos was found in singularly perturbed dynamical systems with periodically [D. Müller et al., Phys. Rev. Lett. 120, 084102 (2018)] and quasiperiodically [D. Müller-Bender and G. Radons, Phys. Rev. E 107, 014205 (2023)] time-varying delay. Compared to high-dimensional turbulent chaos that is typically found in such systems with large constant delay, laminar chaos is a very low-dimensional phenomenon. It is characterized by a time series with nearly constant laminar phases that are interrupted by irregular bursts, where the intensity level of the laminar phases varies chaotically from phase to phase. In this paper, we demonstrate that laminar chaos, and its generalizations, can also be observed in systems with random and chaotically time-varying delay. Moreover, while for periodic and quasiperiodic delays the appearance of (generalized) laminar chaos and turbulent chaos depends in a fractal manner on the delay parameters, it turns out that short-time correlated random and chaotic delays lead to (generalized) laminar chaos in almost the whole delay parameter space, where the properties of circle maps with quenched disorder play a crucial role. It follows that introducing such a delay variation typically leads to a drastic reduction of the dimension of the chaotic attractor of the considered systems. We investigate the dynamical properties and generalize the known methods for detecting laminar chaos in experimental time series to random and chaotically time-varying delay.