We propose and experimentally demonstrate the quasi-superposition quantum-inspired system (QSQS)—a conceptual quantum system for randomness generation built on measuring two conjugate observables of a permutation sorting process: the deterministic permutation count $n_p$ and the fundamentally nondeterministic sorting time $t$. By analogy with quantum systems, these observables are linked by an uncertainty-like constraint: algorithmic determinism ensures structural uniformity, while system-level fluctuations introduce irreducible unpredictability. We realize this framework concretely as a quantum permutation pad (QPP) random number generator (RNG) or QPP-RNG, a system-embedded, software-based true random number generator (TRNG). In QPP-RNG, real-time measurements of sorting time $t$—shaped by CPU pipeline jitter, cache latency, and OS scheduling—dynamically reseed the pseudorandom RNG, driving the permutation sequence. This design fuses deterministic and nondeterministic components, so that entropy emerges organically from the quasisuperposition structure of the system. Crucially, the QSQS transforms initially right-skewed raw distributions of $n_p$ and $t$ into nearly uniform outputs after modulo reduction. This effect arises from the system's internal degeneracies: many distinct internal states collapse into the same output symbol, effectively flattening biases and filling out the output space. This transformation from biased measurements to uniform randomness is the core principle of the QSQS. Empirical results show that as the repetition factor $m$ increases, output entropy converges toward theoretical maxima: Shannon and NIST SP 800-90B min-entropy values approach 8 bits, chi-squared statistics stabilize near ideal uniformity, and bell curve plots visually confirm the flattening from skewed to uniform distributions. The convergence to uniformity occurs at a rate inversely proportional to the size of the permutation space, making the system both scalable and theoretically grounded. Beyond practical implications, our findings illustrate how the QSQS unifies deterministic algorithmic processes with nondeterministic physical fluctuations in a single framework, offering a physics-based perspective for engineering randomness. In the quantum-safe era, the QPP-RNG can close the entropy gap by embedding true randomness directly into cryptographic modules, reducing reliance on external entropy sources and enabling entropy-rich, self-contained postquantum cryptographic ecosystems.

Identifying the universality class of critical active phase transitions has been the subject of recent interest and controversy. Resolving these controversies will require robust numerical investigations to determine whether active critical exponents point to novel universality classes or are consistent with established ones. Here, we conduct large-scale computer simulations and a finite-size scaling analysis of the motility-induced phase separation (MIPS) of active Brownian hard spheres in three dimensions (3D), finding that the static and dynamic critical exponents all closely match those of the 3D Ising universality class with a conserved scalar order parameter. This finding is corroborated by a fluctuating hydrodynamic description of the critical dynamics of the order parameter field which flows to the Wilson-Fisher fixed point in three dimensions. Our work suggests that 3D MIPS and likely the entire phase diagram of active Brownian hard spheres is similar to that of molecular passive fluids despite the absence of Boltzmann statistics.

We investigated thermal transport in aqueous solutions containing short amphiphilic and purely hydrophilic oligomers using hybrid molecular dynamics and multiparticle collision dynamics simulations. By systematically varying the simulation box length, we observed a dimensional crossover from three-dimensional to quasi-one-dimensional behavior, accompanied by a nonlinear increase in thermal conductivity. This transition was characterized by deviations from theoretical temperature profiles and a prolonged decay of heat flux autocorrelation functions, indicating the emergence of anomalous thermal transport. The addition of oligomers, whether amphiphilic or hydrophilic, promoted the emergence of anomalous behavior compared with pure solvent systems. While the formation of spherical micelles by amphiphilic oligomers increased thermal conductivity, it had minimal influence on the scaling behavior associated with anomalous transport, such as $\kappa \sim {\xi }^{1/3}$. These results suggest that geometric anisotropy and the presence of oligomeric solutes are the primary drivers of anomalous thermal transport, whereas self-assembled structures mainly improve thermal transport efficiency. Overall, our findings offer microscopic insights into non-Fourier thermal transport in nanofluids and confined liquid systems and provide a foundation for the rational design of thermally functional materials, where structural organization and transport properties can be tuned synergistically.

The following model is studied analytically and numerically: point particles with masses $m,\mu ,m,\cdots$ ($m\ge \mu$) are distributed over the positive half-axis. Their dynamics is initiated by giving a positive velocity to the particle located at the origin; in its course, the particles undergo elastic collisions. We show that, for certain values of $m/\mu$, starting from the initial state where the particles are equidistant, the system evolves in a hydrodynamic way: (i) the rightmost particle (blast front) moves as $t^{\delta }$ with $\delta <1$; (ii) recoiled particles behind the front enter the negative half-axis; and (iii) the splatter—the particles with locations $x\le 0$—moves in the ballistic way and eventually takes over the whole energy of the system. These results agree with those obtained in S. Chakraborti et al., SciPost Phys. 13, 074 (2022), for $m/\mu =2$, and random initial particle positions. At the same time, we explicitly found the collection of positive numbers $\{{\mathcal{M}}_i,i\in \mathbf{N}\}$ such that, for $m/\mu ={\mathcal{M}}_i, i\le 700$, the following holds: (a) the splatter is absent; (b) the number of simultaneously moving particles is at most three; and (c) the blast front moves in the ballistic way. However, if, similarly as in S. Chakraborti et al., the particle positions are sampled from a uniformly distributed ensemble, for $m/\mu ={\mathcal{M}}_i$ the system evolves in a hydrodynamic way.

We study the large-order behavior of the functional renormalization group (FRG). For a model in dimension zero, we establish Borel summability for a large class of microscopic couplings. Writing the derivatives of FRG as contour integrals, we express the Borel transform as well as the original series as integrals. Taking the strong-coupling limit in this representation, we show that all short-ranged microscopic disorders flow to the same universal fixed point. Our results are relevant for FRG in disordered elastic systems.

We consider the effect of nonreciprocity in a binary mixture of self-propelled particles with antialigning interactions, where a particle of type A reacts differently to a particle of type B than vice versa. Starting from a well-known microscopic Langevin model for the particles, setting up the corresponding exact N-particle Fokker-Planck equation, and making Boltzmann's assumptions of low density and one-sided molecular chaos, the nonlinear active Boltzmann equation with the exact collision operator is derived. In this derivation, the effect of phase-space compression and the buildup of pair correlations during binary interactions is explicitly taken into account, leading to a theoretical description beyond mean field. This extends previous results for reciprocal interactions, where it was found that orientational order can emerge in a system with purely antialigning interactions. Although the equations of motion are more complex than in the reciprocal system, the theory still leads to analytical expressions and predictions. Comparisons with agent-based simulations show excellent quantitative agreement of the dynamic and static behavior in the low-density and/or small coupling limit.

We present a continuous-space realization of the coupled memory graph process, a minimal non-Markovian framework in which coherence emerges through internal feedback. A single Brownian particle evolves on a viscoelastic substrate that records its trajectory as a scalar memory field and exerts local forces via the gradient of accumulated imprints. This autonomous, closed-loop dynamics generates structured, phase-locked motion without external forcing. The system is governed by coupled integro-differential equations: the memory field evolves as a spatiotemporal convolution of the particle's path, while its velocity responds to the gradient of this evolving field. Simulations reveal a sharp transition from unstructured diffusion to coherent burst-trap cycles, controlled by substrate stiffness and marked by multimodal speed distributions, directional locking, and spectral entrainment. This coherence point aligns across three axes: (i) saturation of memory energy, (ii) peak transfer entropy, and (iii) a bifurcation in transverse stability. We interpret this as the emergence of a memory engine—a self-organizing mechanism converting stored memory into predictive motion—illustrating that coherence arises not from tuning, but from coupling.

Anomalous diffusion is an important physical property of active Brownian particles and results mainly from their rich dynamic behavior. We use nonequilibrium molecular dynamics methods to study the mass diffusion of two-dimensional active particles under concentration gradients. It is found that active particles exhibit anomalous collective diffusion behavior that violates Fick's law, whereby their diffusion coefficient diverges as the system size increases. The particles exhibit a flow pattern characterized by large-scale structures, where their movement trajectories and directions are correlated and synchronous. This correlation gives rise to the phenomenon of superdiffusion. This work provides a detailed interpretation of the divergent characteristics and physical mechanisms of active particles based on long-time correlations, velocity spectrum analysis, and local synchronization rates. Our results offer a path for deeply understanding the nonequilibrium dynamic properties of active particles under complex conditions.

Relevant and fundamental concepts of the statistical mechanical theory of classical liquids are ordinarily introduced in the context of the description of thermodynamic equilibrium states. This makes explicit reference to probability distribution functions of equilibrium statistical ensembles (canonical, microcanonical, etc.) in the derivation of general and fundamental relations between interparticle interactions and measurable macroscopic properties of a given system. This includes, for instance, expressing the internal energy and the pressure as functionals of the radial distribution function, or writing transport coefficients (diffusion constant, linear viscosity, etc.) in terms of integral relations involving both static and dynamic autocorrelation functions (density-density, stress-stress, etc.). Most commonly, however, matter is not in thermodynamic equilibrium, and this calls for the extension of these relations to out-of-equilibrium conditions with the aim of understanding, for example, the time-dependent transient states during the process of equilibration, or the aging of glass- and gel-forming liquids during the formation of nonequilibrium amorphous solid states. In this work, we address this issue from both a general perspective and an illustrative concrete application focused on the first-principles description of rheological and viscoelastic properties of glass- and gel-forming liquids.

This study investigates the emergence of symmetry-breaking dynamics and the associated bifurcation behavior in an identically coupled Rosenzweig-MacArthur model with fitness-dependent dispersal between patches. We identify the occurrence of a symmetry-breaking (SB) state, characterized by the difference in the amplitude of oscillations across patches, signifying a form of desynchronization that supports species persistence. As the predator dispersal rate is varied, the SB state undergoes a sequence of dynamical transitions, alternating between chaotic symmetry breaking (CSB) and periodic symmetry breaking (PSB) states, and it includes the emergence of periodic windows that occur within chaotic windows across the dispersal rate. The alternating chaotic and periodic nature of SB dynamics is confirmed with the help of Lyapunov exponent analysis. In addition to the SB state, we observed antiphase synchronized (APS) and in-phase synchronized (IPS) states. To further understand the impact of initial conditions on distinct dynamical outcomes, we explore the basins of attraction within multistable regions. Finally, the stability of the APS, PSB, and IPS states is analyzed using Floquet analysis.

Reservoir computing (RC) exploits the intrinsic dynamics of a chaotic system, called the reservoir, to perform various time-varying functions. An important use-case of RC is the generation of temporal sequences via a trainable output-to-reservoir feedback loop while leaving the reservoir intact, providing a hopeful premise where biological neural networks could harness unstructured groups of neurones for functionality. Despite the promise of RC in various domains, an understanding of why RCs fail in certain scenarios is lacking. Here we formulate an existence condition for a feedback loop that produces the target sequence. We next demonstrate that, given a sufficiently large network reservoir, two separate factors are needed for successful training: global network stability of the target orbit, and the ability of the training algorithm to drive the system close enough to the target, which we term “reach.” By training a reservoir over a range of target output amplitudes and periods, we verify that reach-limited failures depend on the training algorithm while stability-limited failures are invariant across different algorithms. We leverage dynamical mean-field theory to provide an amplitude-period scaling bound on achievable outputs by RC networks and propose a way of enhancing algorithm reach via forgetting. Using the new understanding of RC failure modes, we explore the effect of changing reservoir properties and find that simply scaling up reservoir size results in a stability-reach trade-off across regimes, while introducing distinct neurone types ameliorates the problem. Taken together, the mechanistic understanding of RC performance bounds can guide the future design and deployment of reservoir networks, while also shedding light on how biology might acquire established network characteristics for functional competence.

In a mix of prejudiced and unprejudiced individuals engaged in strategic interactions, the individual intensity of prejudice is expected to influence the overall level of societal prejudice. A high level of prejudice should lead to discrimination that may manifest as unfairness and, perhaps, even spite. In this paper, we investigate this idea in the classical paradigm of the ultimatum game, which we theoretically modify to introduce prejudice at the level of players, terming its intensity as prejudicity. The stochastic evolutionary game dynamics, in the regime of replication-selection, reveals the emergence of spiteful behavior as a dominant behavior via a first-order phase transition—a discontinuous jump in the frequency of spiteful individuals at a threshold value of prejudicity. The phase transition is quite robust and becomes progressively conspicuous in the limit of large population size, where deterministic evolutionary game dynamics, viz., replicator dynamics, approximates the system closely. The emergence of spite driven by prejudice is also found to persist when one considers long-term evolutionary dynamics in the mutation-selection dominated regime.

Autochemotaxis, the directed movement of cells along gradients in chemicals they secrete, is central to the formation of complex spatiotemporal patterns in biological systems. Since the introduction of the Keller-Segel model, numerous variants have been analyzed, revealing phenomena such as coarsening of aggregates, stable aggregate sizes, and spatiotemporally chaotic dynamics. Here we consider general mass-conserving Keller-Segel models, that is, models without cell growth and death, and analyze the generic long-time dynamics of the chemotactic aggregates. Building on and extending our previous work, which demonstrated that chemotactic aggregation can be understood through a generalized Maxwell construction balancing density fluxes and reactive turnover, we use singular perturbation theory to derive the rates of mass competition between well-separated aggregates. We analyze how this mass-competition process drives coarsening in both diffusion- and reaction-limited regimes, with the diffusion-limited rate aligning with our previous quasi-steady-state analyses. Our results generalize earlier mathematical findings, demonstrating that coarsening is driven by self-amplifying mass transport and aggregate coalescence. Additionally, we provide a linear stability analysis of the lateral instability, predicting it through a nullcline-slope criterion that parallels the curvature criterion in spinodal decomposition. Overall, our findings suggest that chemotactic aggregates behave similarly to phase-separating droplets, providing a robust framework for understanding the coarse-grained dynamics of autochemotactic cell populations and a quantitative basis for comparing chemotactic coarsening to canonical nonequilibrium phase separation.

Individual bacterial cells grow and divide stochastically. Yet they maintain their characteristic sizes across generations within a tightly controlled range. What rules ensure intergenerational stochastic homeostasis of individual cell sizes? Valuable clues have emerged from high-precision long-term tracking of individual statistically identical Caulobacter crescentus cells as reported by Joshi et al. [bioRxiv (2023)] and Ziegler et al. [Mol. Biol. Cell 35, ar78 (2024)]: Intergenerational cell-size homeostasis is an inherently stochastic phenomenon, follows Markovian or memory-free dynamics, and cells obey an intergenerational scaling law, which governs the stochastic map characterizing generational sequences of cell sizes. These observed emergent simplicities serve as essential building blocks of the data-informed principled theoretical framework we develop here. Our exact analytic fitting-parameter-free results for the predicted intergenerational stochastic map governing the precision kinematics of cell-size homeostasis are remarkably well borne out by experimental data, including extant published data on other microorganisms, Escherichia coli and Bacillus subtilis. Furthermore, our framework naturally yields the general exact and analytic condition that is necessary and sufficient to ensure that stochastic homeostasis can be achieved and maintained. Significantly, this condition is more stringent than the known heuristic result from quasideterministic frameworks. In turn, the fully stochastic treatment we present here extends and updates extant frameworks and highlights the inherently stochastic behaviors of individual cells in homeostasis.

Spectral line broadening models often make a number of simplifying approximations. The effects of longitudinal plasma oscillations, otherwise known as Langmuir waves, are often ignored or included in a dynamic screening function. We include the effects of plasma oscillations within the foundational work of Bohm and Pines [D. Bohm and D. Pines, Phys. Rev. 82, 625 (1951), D. Pines and D. Bohm, Phys. Rev. 85, 338 (1952), D. Bohm and D. Pines, Phys. Rev. 92, 609 (1953), and D. Pines, Phys. Rev. 92, 626 (1953)]. Our line broadening model, therefore, treats the plasma oscillations quantum mechanically, calculating how a radiating atom interacts with plasmons. We investigate the impact that the plasmons have on the line shape when the plasmons are in thermal equilibrium and when the plasmons are excited. Various aspects of the latter include the impact of the intensity-generating higher-order harmonics, and how the spectrum changes as a function of the intensity distribution of the plasmons. Lastly, we also explore cases of a radiator with forbidden components, such as in He-like structure, as well as a highly charged radiator and how the plasma polarization affects the spectral behavior of the plasmons.

An experiment was performed on the OMEGA EP Laser System to investigate the effects of magnetic fields on laser imprint. A 30 $\mu \mathrm{m}$ thick CH target was driven by a single beam delivering 3.0 kJ of UV energy in a 5 ns square pulse without smoothing by spectral dispersion. The Rayleigh-Taylor amplification of this beam's imprint on the target surface was monitored using face-on gated x-ray radiography from a Gd backlighter. Magnetic fields of up to $45\mathrm{T}$ were applied normal to the target surface. Analysis of the resulting radiographs shows a $60\pm 13\%$ increase in the spectrally resolved surface perturbation amplitudes, consistent at all times and for all unsaturated frequencies. This consistency indicates that the increase in perturbation amplitudes was due to a change in the initial amplitudes rather than Rayleigh-Taylor growth. This is supported by the trajectory of individual modes and the inferred time-averaged perturbation growth rates. Laser imprint is therefore inferred to have increased due to strong magnetic fields that remain in the conduction zone of the target, suppressing off-axis electron motion and limiting the effects of thermal smoothing.

We study, using Discrete Element Method (DEM) simulations, the transient response of an initially steady surface granular flow on a heap of the same material, when the heap is tilted by a small, positive or negative, angle. The system does not have sidewalls, unlike many previous studies. Upon application of the tilt, the height of the free surface, the height of the interface between the flowing and static zones, and the angle of the interface vary exponentially with time while approaching a steady state. A parametric study is conducted considering different mass flow rates, interparticle friction coefficients, particle diameters, and tilt angles. Local rates of erosion and deposition (${\mathrm{\Gamma }}_i,i=e,d$), calculated at the interface, follow predictions of the models of Bouchaud et al. [J. de Phys. I 4, 1383 (1994)] and Boutreux et al. [Phys. Rev. E 58, 4692 (1998)] with ${\mathrm{\Gamma }}_i=v_i(\beta -{\beta }_n)$ where $v_i$ is the erosion velocity, $\beta$ is the angle of the interface, and ${\beta }_n$ is the neutral angle at which there is no erosion or deposition. The erosion velocity $v_e$ is significantly larger than the deposition velocity $v_d$ for all the cases studied, with $v_e/v_d\approx 1.7$. The erosion velocities are nearly independent of the mass flow rate in the layer, the interparticle friction, and the tilt angle. The velocities increase with particle diameter $d$ and flowing layer thickness ${\delta }_i$ as $v_i\sim d^{1/2}{\delta }_i$.

Under high cylindrical confinement, two athermal ring polymers segregate to two halves of the cylinder to maximize their entropy. This has been identified as the primary mechanism of chromosome segregation in cylindrical E. coli cells. In contrast, chromosomes in eukaryotic cells are confined in a spherical nucleus. As ring polymers will remain mixed within spherical confinement, in this work, we provide a simple mechanism to tune entropic interactions and drive organization within the sphere by creating asymmetric topological modifications in the ring-polymer architecture. We introduced cross-links between specific monomers on the ring polymer contour to create a cluster of internal loops connected to a bigger loop. Consequently, we observed an emergent radial organization of the polymer segments in the sphere. For a single topologically modified ring polymer within a sphere, the monomers of the bigger loop were probabilistically found closer to the periphery. However, for multiple such polymers in the sphere, the small loops were localized near the periphery. We considered the bead-spring model of polymers, where there are only repulsive excluded volume interactions between the monomers, ensuring that the observed organization is purely entropy-driven. We also observe a similar organization when we allow topological constraint release by allowing chains to cross each other, as is relevant for chromosome physics. This leads us to a separate investigation where we infer that excluded volume interactions between beads are enough to give a Flory exponent of $0.6$, even if we allow linear polymeric chains to cross each other. Finally, we discuss the plausible relevance of our studies to the organization of euchromatin and the more condensed heterochromatin in eukaryotic chromosomes.

We investigate the flow behavior of highly nonconvex particles on an inclined plane using three-dimensional Contact Dynamics simulations. These particles, termed Platonic polypods, are generated by extruding arms from the faces of Platonic solids, with the number of arms $n_b$ taking values in $\{4,6,8,12,20\}$. Assemblies of these polypods adhere to established flow initiation laws. Interestingly, the onset angle initially decreases with increasing $n_b$ before slightly rising for larger values. Conversely, the maximum angle marking the transition from dense to collisional flow exhibits the opposite trend. As a result, the angular range supporting dense flow widens with increasing $n_b$. In the steady dense flow regime, we analyze the stress, packing fraction, velocity, and connectivity profiles of the assemblies. Away from the boundaries, the granular material exhibits uniform packing fraction, inertial number, and coordination number within the bulk. In this region, the flow follows the classical $\mu \left(I\right)$ rheology. However, near the walls, a “dead zone” emerges, characterized by a localized increase in packing fraction and a sharp reduction in grain velocity. This results in a concave velocity profile over several grain diameters, leading to a breakdown of the $\mu \left(I\right)$ law. A detailed microstructural analysis reveals enhanced interlocking between particles near the walls compared to the bulk. To reconcile the differences between the flowing region and the dead zone, we adapt a recently proposed nonlocal approach, originally developed for rotating drum flows [Wang et al., Phys. Rev. Res. 6, 043310 (2024)], to the inclined plane geometry. This approach relies on a fluidity-based description governed by the local packing fraction. The resulting model, consistent with Bagnold scaling, successfully reproduces the full velocity profiles without requiring any fitting parameters.