# gst: apropos of Parrondo paradox, controlling quantum chaos via Parrondo strategies on noisy intermediate-scale quantum hardware

<< ️Advancements in noisy intermediate-scale quantum (NISQ) computing are steadily pushing these systems toward outperforming classical supercomputers on specific well-defined computational tasks. In this work (AA) explore and control quantum chaos in NISQ systems using discrete-time quantum walks (DTQWs) on cyclic graphs. To efficiently implement quantum walks on NISQ hardware, (They) employ the quantum Fourier transform to diagonalize the conditional shift operator, optimizing circuit depth and fidelity. >>

<< ️(AA) experimentally realize the transition from quantum chaos to order via DTQW dynamics on both odd and even cyclic graphs, specifically 3- and 4-cycle graphs, using the counterintuitive Parrondo paradox strategy across three different NISQ devices. >>

<< ️While the 4-cycle graphs exhibit high-fidelity quantum evolution, the 3-cycle implementation shows significant fidelity improvement when augmented with dynamical decoupling pulses. (Their) results demonstrate a practical approach to probing and harnessing controlled chaotic dynamics on real quantum hardware, laying the groundwork for future quantum algorithms and cryptographic protocols based on quantum walks. >>

Aditi Rath, Dinesh Kumar Panda, Colin Benjamin. Controlling quantum chaos via Parrondo strategies on noisy intermediate-scale quantum hardware. Phys. Rev. E 112, 054219. Nov 18, 2025.

https://journals.aps.org/pre/abstract/10.1103/m89r-2dy5

arXiv: 2506.11225v2 [quant-ph]. Nov 4, 2025.

https://arxiv.org/abs/2506.11225

Also: parrondo, noise, walk, walking, order, chaos, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, parrondo, noise, walk, walking, quantum walk, order, chaos, quantum chaos, transition, dynamical decoupling pulses, cryptography.

# gst: effect of stochasticity on initial transients and chaotic itinerancy for a natural circulation loop.

<< ️The introduction of stochastic forcing to dynamical systems has been shown to induce qualitatively different behaviors, such as attractor hopping, to otherwise stable systems as they approach bifurcation. In this (AA) study, the effect of stochastic forcing on systems that have already undergone bifurcation and evolve on a chaotic attractor is explored. Markov and state-independent models of turbulence-induced stochasticity are developed, and their effects on a natural circulation loop operating in the chaotic regime are compared. >>

<< ️Stochasticity introduces considerable uncertainty into the duration of the initial chaotic transient but tends to accelerate it on average. An Ornstein-Uhlenbeck model of turbulent fluctuations is shown to produce results equivalent to a bootstrapped raw direct numerical simulation signal. >>

<< Similar, though less pronounced, effects are found for systems operating in the chaotic itinerant regime. The Markov model of chaotic itinerancy which is typically applied to this class of problems is shown to be invalid for this system and the Lorenz system, to which it has been applied in the past. >>

<< ️Off-discrete transitions and an upper limit on the time between flow reversals are explained by near misses of the attractor ruins caused by lingering excitation of high-order modes during chaotic itinerancy. >>

John Matulis, Hitesh Bindra. Effect of stochasticity on initial transients and chaotic itinerancy for a natural circulation loop. Phys. Rev. E 112, 044223. Oct 23, 2025

https://journals.aps.org/pre/abstract/10.1103/42pn-wttx

Also: disorder & fluctuations, turbulence, attractor, chaos, transition, uncertainty, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, disorder, fluctuations, turbulence, attractor, chaos, transition, uncertainty, stochasticity, flow instability, chaotic itinerancy, noise-induced transitions.

# gst: a probability space at inception of stochastic process.

<< ️Recently, progress has been made in the theory of turbulence, which provides a framework on how a deterministic process changes to a stochastic one owing to the change in thermodynamic states. It is well known that, in the framework of Newtonian mechanics, motions are dissipative; however, when subjected to periodic motion, a system can produce nondissipative motions intermittently and subject to resonance. It is in resonance that turbulence occurs in fluid flow, solid vibration, thermal transport, etc. In this, the findings from these physical systems are analyzed in the framework of statistics with their own probability space to establish their compliance to the stochastic process. >>

<< ️In particular, a systematic alignment of the inception of the stochastic process with the signed measure theory, signed probability space, and stochastic process was investigated. It was found that the oscillatory load from the dissipative state excited the system and resulted in a quasi-periodic probability density function with the negative probability regimes. In addition, the vectorial nature of the random velocity splits the probability density function along both the positive and negative axes with slight asymmetricity. By assuming that a deterministic process has a probability of 1, (AA) can express the inception of a stochastic process, and the subsequent benefit is that a dynamic fractal falls on the probability density function. Moreover, (They) leave some questions of inconsistency between the physical system and the measurement theory for future investigation. >>

Liteng Yang, Yuliang Liu, et al. A Probability Space at Inception of Stochastic Process. arXiv: 2510.20824v1 [nlin.CD]. Oct 8, 2025.

https://arxiv.org/abs/2510.20824

Also: turbulence, dissipation, intermittency, random, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, turbulence, dissipation, intermittency, randomness, transitions.

# gst: transition to chaos with conical billiards.

<< ️In this paper, (AA) introduced and extensively investigated dynamical billiards on the surface of a cone with a tilted base. Upon varying the cone angle β, corresponding to a deficit angle 

2πχ = 2π(1 − sin(β)), and tilt angle γ, (They) identified three distinct types of trajectories with associated Poincaré map for conical billiards: rim, hourglass, and mixed. >>

<< ️Region I, where Poincaré space consists of rim, hourglass, and mixed trajectories; Region IIB, where Poincaré space consists of only hourglass and mixed trajectories; and Region IIA, in which (They) find choices of γ and χ for which almost all trajectories are strongly mixing. (..) (AA) also developed a scheme for identifying strongly mixing trajectories. >>

<< ️Furthermore, (They) were able to show that a dynamical billiard on a surface with exclusively convex and positive Gaussian curvature in three dimensions can still exhibit ergodic behavior in certain parameter regimes. >>

<< ️A particularly intriguing feature of this system is that by tuning χ and γ, nearly all points in (θ,ϕ) Poincaré space describing conical line segments in between bounces can be placed at the edge between chaotic and integrable dynamics. Thus this work highlights the potential of conical billiards as a model system for exploring intriguing problems inspired by neural networks at the “edge of chaos”. >>

Lara Braverman, David R. Nelson. Transition to chaos with conical billiards. arXiv: 2508.02786v1 [nlin.CD]. Aug 4, 2025. 

https://arxiv.org/abs/2508.02786

Phys. Rev. E 112, 044221. Oct 21, 2025.

https://journals.aps.org/pre/abstract/10.1103/18f7-sqhz

Also: billiard, chaos, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, billiards, conical billiard, chaos, transitions, neural networks

# gst: influence of boundary conditions and interfacial slip to achieve a nonequilibrium steady-state for highly confined flows

<< ️(AA) investigate the equilibration time to attain steady-state for a system of liquid molecules under boundary-driven planar Couette flow via nonequilibrium molecular dynamics (NEMD) simulation. >>

<< ️In particular, (They) examine the equilibration time for the two common types of boundary driven flow: one in which both walls slide with equal and opposite velocity, and the other in which one wall is fixed and the other moves with twice the velocity. Both flows give identical steady-state strain rates, and hence flow properties, but the transient behaviour is completely different. >>

<< ️(They) find that in the case of no-slip boundary conditions, the equilibration times for the counter-sliding walls flow are exactly 4 times faster than those of the single sliding wall system, and this is independent of the atomistic nature of the fluid, i.e., it is an entirely hydrodynamic feature. (They) also find that systems that exhibit slip have longer equilibration times in general and the ratio of equilibration times for the two types of boundary-driven flow is even more pronounced. >>

<< ️(AA) analyse the problem by decomposing a generic planar Couette flow into a linear sum of purely symmetric and antisymmetric flows. (They) find that the no-slip equilibration time is dominated by the slowest decaying eigenvalue of the solution to the Navier-Stokes equation. In the case of slip, the longest relaxation time is now dominated by the transient slip velocity response, which is longer than the no-slip response time. In the case of a high-slip system of water confined to graphene channels, the enhancement is over two orders of magnitude. >>

Carmelo Riccardo Civello, Luca Maffioli, et al. The influence of boundary conditions and interfacial slip on the time taken to achieve a nonequilibrium steady-state for highly confined flows. arXiv: 2509.20944v1 [physics.flu-dyn]. Sep 25, 2025.

https://arxiv.org/abs/2509.20944

Also: transition, fluctuations, slipping, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, transitions, transient behaviours,  fluctuations, thermal fluctuations, slipping, uncertainty, counter-sliding walls.

# gst: extreme vertical drafts as drivers of Lagrangian dispersion in stably stratified turbulent flows.

<< ️The dispersion of Lagrangian particle pairs is a fundamental process in turbulence, with implications for mixing, transport, and the statistical properties of particles in geophysical and environmental flows. While classical theories describe pair dispersion through scaling laws related to energy cascades, extreme events in turbulent flows can significantly alter these dynamics. This is especially important in stratified flows, where intermittency manifests itself also as strong updrafts and downdrafts. >>

<< ️In this study, (AA) investigate the influence of extreme events on the relative dispersion of particle pairs in stably stratified turbulence. Using numerical simulations (They) analyze the statistical properties of pair separation across different regimes, and quantify deviations from classical Richardson scaling. (Their) results highlight the role of extreme drafts in accelerating dispersion. >>

Christian Reartes, Pablo D. Mininni, Raffaele Marino. Extreme vertical drafts as drivers of Lagrangian dispersion in stably stratified turbulent flows. arXiv: 2509.12962v1 [physics.flu-dyn]. Sep 16, 2025.

https://arxiv.org/abs/2509.12962

Also: turbulence, intermittency, chaos, transition, particle, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, turbulence, stratified turbulence,  intermittency, chaos, transitions, particles, extreme events, stratified flows, accelerating dispersion.

# gst: randomness with constraints: constructing minimal models for high-dimensional biology.

<< ️Biologists and physicists have a rich tradition of modeling living systems with simple models composed of a few interacting components. Despite the remarkable success of this approach, it remains unclear how to use such finely tuned models to study complex biological systems composed of numerous heterogeneous, interacting components. >>

<< ️One possible strategy for taming this biological complexity is to embrace the idea that many biological behaviors we observe are ``typical'' and can be modeled using random systems that respect biologically-motivated constraints. Here, (AA) review recent works showing how this approach can be used to make close connection with experiments in biological systems ranging from neuroscience to ecology and evolution and beyond. Collectively, these works suggest that the ``random-with-constraints'' paradigm represents a promising new modeling strategy for capturing experimentally observed dynamical and statistical features in high-dimensional biological data and provides a powerful minimal modeling philosophy for biology. >>

Ilya Nemenman, Pankaj Mehta. Randomness with constraints: constructing minimal models for high-dimensional biology. arXiv: 2509.03765v1 [physics.bio-ph]. Sep 3, 2025.

https://arxiv.org/abs/2509.03765

Also: random, transition, disorder & fluctuations, fly at random, quasi-stochastic poetry, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, randomness, transitions, disorder & fluctuations, random-with-constraints, fly at random, quasi-stochastic poetry.

# brain: self-organized learning emerges from coherent coupling of critical neurons.

<< ️Deep artificial neural networks have surpassed human-level performance across a diverse array of complex learning tasks, establishing themselves as indispensable tools in both social applications and scientific research. >>

<< ️Despite these advances, the underlying mechanisms of training in artificial neural networks remain elusive. >>

<< ️Here, (AA) propose that artificial neural networks function as adaptive, self-organizing information processing systems in which training is mediated by the coherent coupling of strongly activated, task-specific critical neurons. >>

<< ️(AA) demonstrate that such neuronal coupling gives rise to Hebbian-like neural correlation graphs, which undergo a dynamic, second-order connectivity phase transition during the initial stages of training. Concurrently, the connection weights among critical neurons are consistently reinforced while being simultaneously redistributed in a stochastic manner. >>

<< ️As a result, a precise balance of neuronal contributions is established, inducing a local concentration within the random loss landscape which provides theoretical explanation for generalization capacity. >>

<< ️(AA) further identify a later on convergence phase transition characterized by a phase boundary in hyperparameter space, driven by the nonequilibrium probability flux through weight space. The critical computational graphs resulting from coherent coupling also decode the predictive rules learned by artificial neural networks, drawing analogies to avalanche-like dynamics observed in biological neural circuits. >>

<< ️(AA) findings suggest that the coherent coupling of critical neurons and the ensuing local concentration within the loss landscapes may represent universal learning mechanisms shared by both artificial and biological neural computation. >>

Chuanbo Liu, Jin Wang. Self-organized learning emerges from coherent coupling of critical neurons. arXiv: 2509.00107v1 [cond-mat.dis-nn]. Aug 28, 2025.

https://arxiv.org/abs/2509.00107

Also: brain, neuro, network, random, transition, ai (artificial intell) (bot), in https://www.inkgmr.net/kwrds.html 

Keywords: gst, brain, neurons, networks, randomness, transitions, ai (artificial intell) (bot), learning mechanisms, self-organized learning, artificial neural networks, deep learning, neuronal coupling, criticality, stochasticity, avalanche-like dynamics.

# gst: a journey into billiard systems

<< ️Have you ever played or watched a game of pool? If so, you have already seen a billiard system in action. In mathematics and physics, a billiard system describes a ball that moves in straight lines and bounces off walls. Despite these simple rules, billiard systems can produce remarkably rich behaviors: some table shapes generate regular, periodic patterns, while others give rise to complete chaos. >>

<< Scientists also study what happens when (They) shrink the ball down to the size of an electron to a world where quantum effects take over and the familiar reflection rules no longer apply. >>

<< ️In this article, (AA) discuss billiard systems in their many forms and show how such a simple setup can reveal fundamental insights into the behavior of nature at both classical and quantum scales. >>

Weiqi Chu, Matthew Dobson. What Do Bouncing Balls Tell Us About the Universe? A Journey into Billiard Systems. arXiv: 2508.18519v1 [math.DS]. Aug 25, 2025.

https://arxiv.org/abs/2508.18519

Also: billiard, transition, chaos, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, billiard, transition, chaos.

# gst: falling viscoelastic liquid films on a slippery substrate.

<< This (AA) study develops a weighted-residual model for Oldroyd-B films on slippery substrates at moderate Reynolds number and large slippery length. >>

<< Linear stability analysis reveals that wall slip promotes perturbation growth rates, increases cut-off wave numbers, and accelerates long-wave propagation speed, demonstrating a destabilizing effect. Two distinct families of traveling waves are sought, which demonstrate that varying the slippery length can alter the bifurcation type of traveling wave families. >>

<< Particularly, large slippery length can cause the transition of drag-gravity regime into the drag-inertia regime. In the drag-gravity regime, slippery effect promotes the wave speed and height. However, in the drag-inertia regime, slippery effect can suppress the wave height even though the wave propagates faster. >>

<< Interestingly, plateau-type waves (They)  found in the Oldroyd-B film flow at large slippery length, which has not been reported previously. >>

Zhiwei Song, Zijing Ding. Falling viscoelastic liquid films on a slippery substrate. Phys. Rev. E 112, 025106. Aug 25, 2025. 

https://journals.aps.org/pre/abstract/10.1103/vv3p-cvk2

Also: slipping, waves, instability, transition,   in https://www.inkgmr.net/kwrds.html 

Keywords: gst, slipping, slippery substrates, waves, instability, instability of free-surface flows, transitions.

# gst: noisy active matter

<< ️Noise threads every scale of the natural world. Once dismissed as mere background hiss, it is now recognized as both a currency of information and a source of order in systems driven far from equilibrium. >>

<< ️From nanometer-scale motor proteins to meter-scale bird flocks, active collectives harness noise to break symmetry, explore decision landscapes, and poise themselves at the cusp where sensitivity and robustness coexist. >>

<< ️(AA) review the physics that underpins this paradox: how energy-consuming feedback rectifies stochastic fluctuations, how multiplicative noise seeds patterns and state transitions, and how living ensembles average the residual errors. Bridging single-molecule calorimetry, critical flocking, and robophysical swarms, (They) propose a unified view in which noise is not background blur but a tunable resource for adaptation and emergent order in biology and engineered active matter. >>

Atanu Chatterjee, Tuhin Chakrabortty, Saad Bhamla. Noisy active matter. arXiv:2508.16031v1 [cond-mat.soft]. Aug 22, 2025.

https://arxiv.org/abs/2508.16031

Also: transition, noise, track changes in noise, erratic, random, error, mistake, uncertainty, disorder & fluctuations, walk, walking, dance, jazz, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, transitions, noise, track changes in noise, erratic, random, error, mistake, uncertainty, disorder & fluctuations, deposition (analogy, abstraction), walk, walking, life, dance, jazz. 

# gst: apropos of (unexpected?) transitions; the bizarre role of noise as operational control

<< ️Stochastic systems have a control-theoretic interpretation in which noise plays the role of control. In the weak-noise limit, relevant at low temperatures or in large populations, this leads to a precise mathematical mapping: The most probable trajectory between two states minimizes an action functional and corresponds to an optimal control strategy.  >>

<< ️In Langevin dynamics, the noise term itself serves as the control. For general Markov jump processes, such as chemical reaction networks or electronic circuits, (AA) use the Doi-Peliti formalism to identify the “response” (or “momentum”) field 𝜋 as the control variable. This resolves a long-standing interpretational problem in the field-theoretic description of stochastic systems: Although 𝜋 evolves backward in time, it has a clear physical role as the control that steers the system along rare trajectories. >>

<< ️This implies that nature is constantly sampling control strategies.  >>

<< ️(AA) illustrate the mapping on multistable chemical reaction networks, systems with unstable fixed points, and specifically on stochastic resonance and Brownian ratchets. >>

<< ️ The noise-control mapping justifies agential descriptions of these phenomena and builds intuition for otherwise puzzling phenomena of stochastic systems: why probabilities are generically nonsmooth functions of state out of thermal equilibrium; why biological mechanisms can work better in the presence of noise; and how agential behavior emerges naturally without recourse to mysticism. >>

Eric De Giuli. Noise equals control. Phys. Rev. E 112, 024142. Aug 29, 2025.

https://journals.aps.org/pre/abstract/10.1103/vlx8-spc6

arXiv:2503.15670v3 [q-bio.MN]. 

https://arxiv.org/abs/2503.15670

Also: transition, noise, track changes in noise, erratic, random, error, mistake, uncertainty, disorder & fluctuations, walk, walking, dance, jazz, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, transition, noise, track changes in noise, erratic, random, error, mistake, uncertainty, disorder & fluctuations, deposition (analogy, abstraction), walk, walking, life, dance, jazz. 

# gst: H.v.Foerster's principle revisited, 'allostasis' theory reconsiders 'order through noise'

<< ️The notion of homeostasis typically conceptualises biological and artificial systems as maintaining stability by resisting deviations caused by environmental and social perturbations. In contrast, (social) allostasis proposes that these systems can proactively leverage these very perturbations to reconfigure their regulatory parameters in anticipation of environmental demands, aligning with von Foerster's ``order through noise'' principle. >>

<< ️This (AA) paper formulates a computational model of allostatic and social allostatic regulation that employs biophysiologically inspired signal transducers, analogous to hormones like cortisol and oxytocin, to encode information from both the environment and social interactions, which mediate this dynamic reconfiguration. >>

<< ️ The (AA) results show that allostatic and social allostatic regulation enable agents to leverage environmental and social ``noise'' for adaptive reconfiguration, leading to improved viability compared to purely reactive homeostatic agents. >>

<< ️This (AA) work offers a novel computational perspective on the principles of social allostasis and their potential for designing more robust, bio-inspired, adaptive systems. >>

Imran Khan. [Social] Allostasis: Or, How I Learned To Stop Worrying and Love The Noise. arXiv: 2508.12791v1 [cs.AI]. Aug 18, 2025. 

https://arxiv.org/abs/2508.12791

Also: noise, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, noise, adaptations, transitions, allostasis, homeostasis, life.

# gst: hidden qu-classical correspondence in chaotic billiards revealed by mutual information.

<< ️Avoided level crossings, commonly associated with quantum chaos, are typically interpreted as signatures of eigenstate hybridization and spatial delocalization, often viewed as ergodic spreading. >>

<< ️(AA) show that, contrary to this expectation, increasing chaos in quantum billiards enhances mutual information between conjugate phase space variables, revealing nontrivial correlations. Using an information-theoretic decomposition of eigenstate entropy, (They) demonstrate that spatial delocalization may coincide with increased mutual information between position and momentum. >>

<< These correlations track classical invariant structures in phase space and persist beyond the semiclassical regime, suggesting a robust information-theoretic manifestation of quantum-classical correspondence. >>

Kyu-Won Park, Soojoon Lee, Kabgyun Jeong. Hidden quantum-classical correspondence in chaotic billiards revealed by mutual information. Phys. Rev. E 112, 024209. Aug 13, 2025.

https://journals.aps.org/pre/abstract/10.1103/qpxx-csdj

arXiv:2505.08205v1 [nlin.CD]. May 13, 2025.

https://arxiv.org/abs/2505.08205

Also: billiard, chaos, waves, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, billiard, chaos, qu-chaos, waves, quantum-to-classical transition

# gst: an analysis of the phenomenon of chaotic itinerancy.

AA << introduce a new methodology for the analysis of the phenomenon of chaotic itinerancy in a dynamical system using the notion of entropy and a clustering algorithm. (They) determine systems likely to experience chaotic itinerancy by means of local Shannon entropy and local permutation entropy. In such systems, we find quasi-stable states (attractor ruins) and chaotic transition states using a density-based clustering algorithm. >>

Their << ️approach then focuses on examining the chaotic itinerancy dynamics through the characterization of residence times within these states and chaotic transitions between them with the help of some statistical tests. The effectiveness of these methods is demonstrated on two systems that serve as well-known models exhibiting chaotic itinerancy: globally coupled logistic maps (GCM) and mutually coupled Gaussian maps. >>

<< ️Although the phenomenon of chaotic itinerancy is often associated with high dimensional systems, (They) were able to provide evidence for the presence of this phenomenon in the studied low-dimensional systems. >>

Nikodem Mierski, Paweł Pilarczyk. Analysis of the Chaotic Itinerancy Phenomenon using Entropy and Clustering. arXiv: 2507.22643v1 [nlin.CD]. Jul 30, 2025. 

https://arxiv.org/abs/2507.22643

Also: chaos, intermittency, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chaos, intermittency, transitions, chaotic itinerancy, low-dimensional systems.

# gst: topologically nontrivial multicritical points.

<< ️Recently, the intriguing interplay between topology and quantum criticality has been unveiled in one-dimensional topological chains with extended nearest-neighbor couplings. In these systems, topologically distinct critical phases emerge with localized edge modes despite the vanishing bulk gap. >>

<< ️In this work, (AA) study the topological multicritical points at which distinct gapped and critical phases intersect. Specifically, (They) consider a topological chain with coupling up to the third nearest neighbors, which shows stable localized edge modes at the multicritical points. These points possess only nontrivial gapped and critical phases around them and are also characterized by the quadratic dispersion around the gap-closing points. >>

<< Further, (AA) analyze the nature of zeros in the vicinity of the multicritical points by calculating the discriminants of the associated polynomial. The discriminant uniquely identifies the topological multicritical points and distinguishes them from the trivial ones.  >>

AA << finally study the robustness of the zero-energy modes at the multicritical points at weak disorder strengths, and reveal the presence of a topologically nontrivial gapless Anderson-localized phase at strong disorder strengths. >>

Ranjith R Kumar, Pasquale Marra. Topologically nontrivial multicritical points. arXiv: 2507.11120v1 [cond-mat.dis-nn]. Jul 15, 2025.

https://arxiv.org/abs/2507.11120

Also: disorder & fluctuations, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, disorder, disorder & fluctuations, criticality, multicritical points, transition.

# gst: apropos of drift surfaces, e.g., banana orbits, perturbed toroidal vortices display internal simply connected topology.

<< ️This (AA) work shows that the interiors of perturbed zero-helicity vortices display simply connected topology with a crescent-shaped boundary. Flux surfaces in fluid and magnetic vortices were explored analytically, while particle trajectories in the context of plasma confinement were examined numerically, demonstrating the existence of both toroidal and simply connected topologies. >>

<< ️Numerical simulations of particle trajectories were conducted in the context of fusion confinement to calculate particle trajectories in a perturbed Soloviev equilibrium where simply connected flux surfaces were observed. The orbits often displayed crescent shapes, yet showed several marked differences from the flux surfaces, e.g., gyro-radii of size comparable to the crescent diameter, asymmetric crescents, connections between well-separated crescent tips, and possibly toroidal shapes, with an inversion of the roles played by the major and minor axes. >>

<< ️This new topology appears for perturbations in a broad class, with amplitudes and spatial variance allowed to be arbitrarily small. A corollary of this work proves the closedness of field lines under odd-parity perturbations of zero-helicity vortices. >>

Taosif Ahsan, Samuel A. Cohen, Alan H. Glasser. Perturbed Toroidal Vortices Display Internal Simply Connected Topology. arXiv: 2507.04596v1 [math-ph]. Jul 7, 2025. 

https://arxiv.org/abs/2507.04596

Also: vortex, particle, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, vortex, particle, transition, foliated torus, toroidal vortices, banana orbits. 

# gst: noise reinstates collapsed populations; stochastic reversal of deterministic extinction.

<< ️Conventional wisdom suggests that environmental noise drives populations toward extinction. In contrast, (AA) report a paradoxical phenomenon in which stochasticity reverses a deterministic tipping point, thereby preventing collapse. Using a hybrid model that integrates logistic growth with a density-triggered sigmoidal collapse, (They) uncover a striking reversal: deterministic fragility on one side, and stochastic rescue under weak noise on the other. >>

AA << analysis demonstrates that noise disrupts the convergence of deterministic trajectories toward extinction by altering the phase space topology, enabling back-transitions to viable states. This mechanism gives rise to noise-induced metastability and reveals a form of stochastic robustness not captured by deterministic models. >>

<< ️These findings suggest that natural fluctuations can serve as a stabilizing force in complex systems, offering a compelling counter-narrative to classical models in ecology, epidemiology, and beyond. (AA) advocate for a re-evaluation of stabilization strategies, emphasizing the constructive role of stochasticity in averting population collapse. >>

Vinesh Vijayan, B Priyadharshini, et al. Noise reinstates collapsed populations: stochastic reversal of deterministic extinction. arXiv:2507.03954v1 [q-bio.PE]. Jul 5, 2025.

https://arxiv.org/abs/2507.03954

Also:  noise, weak, disorder & fluctuations, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, noise, weakness, disorder,  

fluctuations, tipping point, transitions, stochasticity, stochastic reversal, stochastic rescue. 

# gst: apropos of ghost entities, criticality governs response dynamics and entrainment of periodically forced ghost cycles.

<< ️Many natural and engineered systems display oscillations that are characterized by multiple timescales. Typically, such systems are described as slow-fast systems, where the slow dynamics result from a hyperbolic slow manifold that guides the movement of the system's trajectories. Recently, (AA) have provided an alternative description in which the slow timescale results from Lyapunov-unstable transient dynamics of connected dynamical ghosts that form a closed orbit termed ghost cycle. >>

Here, AA << investigate the response properties of both types of systems to external forcing. Using the classical Van der Pol oscillator and modified versions of this model that correspond to a one-ghost and a two-ghost cycle, respectively, (They) find significant differences in the responses of slow-fast systems and ghost cycles, including increased entrainment regions of the latter. Nonautonomous model analysis reveals that the differences stem from a continuous remodeling of the attractor landscape of the ghost cycle models, enabled by being organized close to saddle-node on invariant cycle bifurcations, in contrast to a qualitatively unaltered attractor landscape of the slow-fast system. >>

(AA) << ️further demonstrate that the observed features occur in various systems with ghost cycles regardless of the exact mathematical model formulation leading to those ghost cycles, making them likely to apply to many other models with ghost cycles across different disciplines and contexts. (They) thus propose that systems containing ghost cycles display increased flexibility and responsiveness to continuous environmental changes. >>

Daniel Koch, Ulrike Feudel, Aneta Koseska. Criticality governs response dynamics and entrainment of periodically forced ghost cycles. Phys. Rev. E 112, 014205. Jul 8, 2025.

https://journals.aps.org/pre/abstract/10.1103/3d9z-qrb1

Also: transition, attractor, self-assembly, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, transition, attractor, self-assembly, bifurcations, saddle-node, synchronization, criticality, self-organized criticality.

# gst: wave-kinetic dynamics of forced-dissipated turbulent internal gravity waves

<< Internal gravity waves are an essential feature of stratified media, such as oceans and atmospheres. >>

<< To investigate their dynamics, (AA) perform simulations of the forced-dissipated kinetic equation describing the evolution of the energy spectrum of weakly nonlinear internal gravity waves. >>

<< During the early evolution, three well-known nonlocal interactions, the elastic scattering, the induced diffusion, and the parametric subharmonic instability, together with a superharmonic resonance play a prominent role. >>

<< In contrast, local interactions are responsible for anisotropic energy cascade on longer timescales. >>

AA << reveal emergence of a condensate at small horizontal wave vectors that can be interpreted as a pure wave-wave interaction-mediated layering process. >>

Vincent Labarre, Giorgio Krstulovic, Sergey Nazarenko. Wave-Kinetic Dynamics of Forced-Dissipated Turbulent Internal Gravity Waves. Phys. Rev. Lett. 135, 014101. Jul 1, 2025.

https://journals.aps.org/prl/abstract/10.1103/b82h-z21n

arXiv:2407.11469v3 [physics.flu-dyn]. Mar 28, 2025.

https://arxiv.org/abs/2407.11469

Also: waves, weak, turbulence, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, weakness, turbulence, transitions, stratified turbulence, wave-turbulence interactions, weak turbulence.