# gst: interwoven long-range order induced by random fields.

<< (AA) propose a distinct type of long-range ordered phase that can occur in classical and quantum many-particle systems. It is induced by impurities and defects that locally break a subset of the order-parameter symmetries, i.e., by random-field disorder that couples to a composite vestigial order parameter. >>

<< The proposed ``implectic'' phase is characterized by spontaneous symmetry breaking on the background of the spatially interwoven domain structure created by the random fields. (They) explicitly demonstrate the existence of this phase in a layered J1−J2 Ising magnet by means of large-scale Monte Carlo simulations. (AA) then discuss numerous potential applications in systems featuring charge and spin density wave order including frustrated magnets, cuprate and iron-based superconductors, and ultracold atoms. >>

Jeremiah Bender, Thomas Vojta. Interwoven long-range order induced by random fields. arXiv: 2607.10337v1 [cond-mat.dis-nn]. Jul 11, 2026.

https://arxiv.org/abs/2607.10337

Also: particle, waves, order, disorder, fracture, crack, random, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particle, waves, order, disorder, fracture, crack, transitions, impurities, defects, locally break, spontaneous symmetry breaking, random-field disorder, implectic long-range ordered phases.

# gst: twisted state stability under local order parameter adaptation.

<< ️Twisted states commonly arise in nonlocally coupled ring networks. (AA) study the stability of twisted states in networks with higher-order interactions under the adaptive mechanism based on the local order parameter. >>

<< ️The adaptive feedback dynamically regulates the coupling strength and thus reshapes the collective dynamics of the system. Analytical and numerical results show that higher-order adaptivity reduces the linear stability of twisted states, whereas pairwise adaptivity enhances it. Numerical simulations further demonstrate that increasing the exponent of higher-order adaptation drives the system toward more ordered states and correspondingly enlarges the basin of twisted states. >>

<< Moreover, a larger coupling range reduces twisted-state stability, while in random hypergraphs, higher-order adaptivity enlarges the synchronization basin without significantly changing the linear stability. These findings reveal a nonequilibrium relationship between linear stability and basin stability and highlight the important role of adaptive regulation in higher-order network dynamics. >>

Xueqin Wang, Hong He, Wende Tang, et al. Twisted state stability under local order parameter adaptation. Phys. Rev. E 114, 014209. Jul 13, 2026. 

https://journals.aps.org/pre/abstract/10.1103/p2wd-nfbr

Also: network, stability, chimera, order, disorder, fluctuations, random, twist, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, stability, chimera, order, disorder, fluctuations, randomness, synchronization, coupled oscillators, adaptive feedbacks, twisted states, basin stability. 

# gst: spatially heterogeneous noise restructures flocking into geometry-locked and vortex states.

<< ️Spatially heterogeneous environments continually challenge the ability of active matter to sustain coherent collective motion. Understanding how collective motion remains robust under changing environments is central to both the functioning of biological systems and the design of smart active matter. >>

<< ️Here, (AA) extend the Vicsek model to include a circular non-noisy region surrounded by a noisy environment - a configuration in which the noise difference sets up a contrast in local directional order between the two regions. (They) find that, as the surrounding noise is increased, the system passes through three distinct dynamical regimes: (i) conventional global flocking at low noise; (ii) geometry-locked motion, aligned with simulation boundaries, at intermediate noise; and (iii) vortical motion within the non-noisy region at high noise. >>

<< Extending the environment to multiple non-noisy regions, (AA) find that the geometry-locked regime can develop a directional coupling, while the vortex mode leads to antiferromagnetic order between the regions. Taken together, (Their) results demonstrate that the spatial modulation of order and disorder offers a powerful and generic strategy for steering active matter, aligning with recent experimental observations of active particles in patterned landscapes. >>

Ankush Semwal, Mahak Poonia, Pintu Patra. Spatially heterogeneous noise restructures flocking into geometry-locked and vortex states. arXiv: 2607.05870v1 [cond-mat.soft]. Jul 7, 2026.

https://arxiv.org/abs/2607.05870

Also: particle, noise, vortex, order, disorder, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particle, noise, vortex, order, disorder, active matter, steering active matter, coherent collective motion, noisy environment, vortical motion, geometry-locked regime. 

# gst: hyperuniform systems are maximally irreversible.

<< ️Hyperuniform systems, defined by the anomalous suppression of large-scale density fluctuations, are a paradigm of non-equilibrium self-assembly. While mechanisms underlying the self-assembly of hyperuniform states have been widely studied, the energetics of this process remain unexplored. This raises a fundamental question: what is the energetic cost of self-assembling a hyperuniform system? >>

<< ️Here, (AA) address this question across several noisy particle systems drawn from soft matter and machine learning, in which hyperuniformity can be induced by tuning noise correlations. Despite their distinct microscopic dynamics, (They) uncover a universal behavior across all systems: hyperuniform states are maximally irreversible, as quantified by the entropy production rate. >>

<< ️Further, (AA) develop a path integral formulation of the entropy production rate directly from the microscopic dynamics, which explains (Their) observations. (AA) work establishes a direct link between emergent long-range structure and time irreversibility and opens a new avenue of probing the energetic cost of hyperuniform self-assembly, ubiquitous across physics, biology, and materials science. >>

Mathias Casiulis, Satyam Anand, Stefano Martiniani. Hyperuniform systems are maximally irreversible.  arXiv: 2607.07411v1 [cond-mat.soft]. Jul 8, 2026.

https://arxiv.org/abs/2607.07411

Also: particle, disorder & fluctuations, self-assembly, noise, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particles, fluctuations, self-assembly, noise, transitions, tuning noise correlations, entropy production rate, long-range structure.

# life: apropos of anomalous (meta)mechanical responses, from active to odd to smart matter.

<< ️The study of active matter has reshaped our understanding of collective states of matter far from equilibrium by proving that energy pumped into the microscopic scale leads to order on the macroscopic scale, collective motion, and anomalous mechanical responses. >>

<< More recently, the discovery of odd elasticity and nonreciprocal mechanical couplings has extended these ideas to solid-like active systems, revealing materials with nonconservative elastic response. >>

<< ️Simultaneously, innovative developments in swarm robotics, programmable metamaterials, and learning algorithms have led to the emergence of a new frontier in which collective behavior and mechanical response are no longer fixed by design, but adapted, optimized, and learned toward functional goals. >>

<< ️This perspective proposes a unifying trajectory, from active to odd to smart matter, organized along two intertwined axes: the traditional gas-liquid-solid progression of condensed matter, and the more recent paradigm shift from spontaneous collective dynamics to task-driven functionality. >> 

<< ️(AA) try to highlight emerging principles, conceptual shifts, and open challenges that come along this trajectory, and argue that learning may play the role of a specific form of emergence, which could advantageously replace the more traditional view of control, at least in the realm of physics. >>

Olivier Dauchot. From active to odd to smart matter. Phys. Rev. E 114, 011001. Jul 8, 2026.

https://journals.aps.org/pre/abstract/10.1103/tzyr-t47w

arXiv: 2607.06051v1 [cond-mat.soft]. Jul 7, 2026.

https://arxiv.org/abs/2607.06051

Also: 'a sciogliere nella metaciotola l' eccessivo rigido neurodistico ...', in: Voli in codice quasistocastico. Notes (quasistochastic poetry). Dec 09, 2004.

https://inkpi.blogspot.com/2004/12/1798-voli-in-codice-quasistocastico.html

Also: Anagrammanti neurali. Notes (quasistochastic poetry). Sep 09, 2006.

https://inkpi.blogspot.com/2006/09/2056-anagrammanti-neurali.html

Also: self-assembly, elastic, disorder, swarm, swarmalators, ai (artificial intell) (bot), brain, game, in https://www.inkgmr.net/kwrds.html 

Keywords: life, self-assembly, elasticity, disorder, swarm, swarmalators, ai,  artificial intelligence, bot, brain, games, active matter, collective states, anomalous responses, odd elasticity, nonreciprocal couplings, nonconservative elastic response, spontaneous collective dynamics, task-driven functionality, learning as a specific form of emergence, learning & adaptation without a brain.

# gst: dynamics of coupled stochastic van der Pol oscillators; bifurcations, synchronization and chaos.

<< ️This (AA) work presents a comprehensive analysis of coupled stochastic van der Pol oscillators, a paradigm for understanding synchronization, bifurcations, and chaos in nonlinear systems subject to random fluctuations. The system comprises two or more oscillators with nonlinear damping, linear diffusive coupling, and additive Gaussian white noise. >>

<< ️(AA) develop a unified framework that systematically connects global bifurcations, synchronization phenomena, and chaotic dynamics within a single coherent stochastic model. (They) explore the stochastic dynamics of coupled van der Pol oscillators by seamlessly blending theoretical principles with in-depth numerical simulations. This integrated approach forms a robust framework for analysis, with essential phenomena clearly depicted in the accompanying figures. (AA) then extend this framework to a comprehensive investigation of large networks, focusing on their continuum limit, emergent pattern formation, the role of noise, and the onset of collective chaos. >>

Shenglan Yuan, Xiang Zhou. Dynamics of Coupled Stochastic van der Pol Oscillators: Bifurcations, Synchronization and Chaos.  arXiv: 2606.31445v1 [nlin.CD]. Jun 30, 2026. 

https://arxiv.org/abs/2606.31445v1

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

Keywords: gst, chaos, noise, randomness, disorder, fluctuations, coupled stochastic van der Pol oscillators, synchronization, bifurcations, emergent pattern formation, collective chaos.

# gst: localization pattern of a mobile impurity in the disordered Kitaev chain.

<< (AA) study a mobile impurity coupled to a Kitaev chain with chemical-potential disorder and ask whether the impurity behavior distinguishes different regimes of the host system. Exact diagonalization calculations for small periodic chains shows that in the deep topological regime the impurity localizes only partially, with a smooth increase of IPR_d, whereas in the deep trivial regime it undergoes a much sharp transition to nearly single-site localization. >>

<< For open chains at strong interaction, DMRG shows edge-localized impurity density near the Kitaev sweet spot. With increasing chemical potential, the impurity weight spreads into the bulk and eventually becomes almost uniform. (They) explain the edge preference analytically from the Majorana-dimer structure: a bulk impurity rearranges two neighboring dimers, while an edge impurity affects only one. >>

<< Disorder competes with this clean edge bias and can pin the impurity in the bulk. Thus, the impurity is sensitive to the regime of the host system, although (AA) do not find a strict one-to-one correspondence between the impurity localization pattern and the host topology. Instead, the disorder-averaged behavior suggests only an indirect correlation between impurity localization and the underlying phase of the chain. >>

A.V. Sadovnikov, A.N. Rubtsov. 

Localization pattern of a mobile impurity in the disordered Kitaev chain. arXiv: 2606.21499v1 [cond-mat.str-el]. Jun 19, 2026.

https://arxiv.org/abs/2606.21499

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

Keywords: gst, disorder, disorder & fluctuations, mobile impurity, bulk impurity, edge impurity, deep topological regime, deep trivial regime. 

# gst: oscillating concentrations suppress condensate coarsening.

<< ️Living cells utilize condensates to spatially concentrate molecules in response to dynamic signals. For instance, nuclear condensates respond to oscillations in transcription factor levels in the nucleoplasm, including those involved in repairing multiple DNA breaks. >>

<< ️To understand how oscillating signals affect condensates, (AA) analyze a theoretical model using numerical simulations and analytical theory. While passive dynamics would drive all molecules into a single condensate, (They) find that sufficiently fast oscillations stabilize multiple droplets, allowing control of their sizes. (They) thus reveal a new behavior of chemically active droplets, which could be exploited in synthetic applications. >>

Mathias S. Heltberg, Lukas H. Kristensen, Mogens H. Jensen, David Zwicker. Oscillating concentrations suppress condensate coarsening. arXiv: 2606.16614v1 [physics.bio-ph]. Jun 15, 2026.

https://arxiv.org/abs/2606.16614

Also: drop, droplet, droploid, self-assembly, disorder & fluctuations, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, drop, droplet, droploid, self-assembly, disorder & fluctuations, chemically active droplets, spatially concentration, nuclear condensate. 

# gst: dissipation-coherence tradeoff for stochastic oscillations.

<< ️Autonomous noisy oscillations in biochemical and mesoscopic systems require nonequilibrium driving and therefore dissipation. A striking conjecture by Oberreiter, Barato, and Seifert (OBS) proposes a universal lower bound on the entropy produced per oscillation period in terms of the coherence number of the slowest oscillatory mode (L. Oberreiter et al. [Phys. Rev. E 106, 014106 (2022)]). >>

<< ️Here (AA) derive a weaker but rigorous lower bound that preserves the OBS structure while introducing a mode-uniformity factor that quantifies how evenly the oscillatory eigenmode is distributed across states in the steady-state inner product. The result makes explicit that an eigenvalue-only prefactor can fail when the dominant oscillatory mode is localized. >>

<< ️(They) also outline a proof-of-principle route for estimating this factor from low-dimensional data under single-mode dominance and sufficiently informative measurements, and derive an eigenvector-free corollary using only the smallest stationary probability. >>

<< ️Translation-invariant Markov jump processes on a ring provide a symmetry-protected class with 𝜂=1, so the refinement reduces to the OBS form; the drift-diffusion limit on a circle saturates the bound. >>

Jie Gu. Dissipation-coherence tradeoff for stochastic oscillations. Phys. Rev. E 113, 064130.  Jun 15, 2026.

https://journals.aps.org/pre/abstract/10.1103/zxw1-zdb7

arXiv: 2606.05498v1 [cond-mat.stat-mech]. Jun 3, 2026.

https://arxiv.org/abs/2606.05498

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

Keywords: gst, noise, disorder, dissipation, entropy, stochasticity, stochastic processes, autonomous noisy oscillations, stochastic oscillations, disorder-induced localization, time series analysis, transitions.

# gst: collective drift and pinning in active rotator networks with Kuramoto coupling and mixed-sign feedback disorder.

<< ️Active rotator models provide a minimal phase description of excitable and oscillatory systems, and have long been used to study mutual entrainment, synchronization, and collective transitions. >>

<< ️Here, (AA) investigate fully connected active rotator networks with Kuramoto coupling, where a common intrinsic drive competes with local feedback amplitudes drawn from a zero-mean Gaussian distribution. This produces a competition between local pinning and collective phase alignment. >>

<< ️Using mean absolute late-time drift and the fractions of positive and negative drifting oscillators, (They) construct numerical regime maps in the feedback-disorder-coupling plane. At weak coupling, increasing the feedback disorder strength suppresses drift, while stronger coupling can restore positive late-time drift when feedback disorder is not too strong. (They) interpret these regimes using analytical limits for the uncoupled and coherent strong-coupling cases. >>

<< ️(They) also examine finite-size effects and zero-mean distributed intrinsic frequencies. Together, these results show that mixed-sign local feedback alone can reshape the balance between pinning and drifting in coupled active rotator networks, even when the intrinsic drive is homogeneous. >>

Arpan Dey. Collective drift and pinning in active rotator networks with Kuramoto coupling and mixed-sign feedback 

disorder. arXiv: 2606.10032v1 [nlin.AO]. Jun 8, 2026.

https://arxiv.org/abs/2606.10032

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

Keywords: gst, networks, disorder, transitions, active rotator networks, excitable- oscillatory- systems, Kuramoto coupling, local feedbacks, feedback disorder.

# gst: localization of active particles on random arrays of parallel filaments.

<< ️Quenched disorder in the environment can fundamentally alter transport dynamics in both active and passive systems. (AA) explore how disordered arrays of filaments govern the distribution of intermittently moving particles which switch between diffusive and processive transport. >>

<<️ Motivated by the mixed-polarity arrangements of parallel microtubules observed in mammalian dendrites, (They) show that such arrays tend to result in localization of particles at regions of convergent filament orientation. In the rapid attachment-detachment limit, the disordered system can be described by a noisy one-dimensional effective energy landscape, whose structure is approximated by a random walk. >>

<< ️The depth and width of wells on this landscape are expressed as a function of the transport kinetics and system geometry. Localization is shown to be strongest at intermediate run-lengths, where biased transport persists long enough to sense the quenched filament polarity but not so long as to facilitate escape from local traps. >>

<< ️These (AA) results demonstrate robust localization of particles moving on random filament networks, highlighting the emergent spatial organization that arises from an interplay of active transport and quenched disorder. >>

Owen Santoso, Elena Koslover. Localization of Active Particles on Random Arrays of Parallel Filaments. arXiv: 2606.00286v1 [cond-mat.dis-nn]. May 29, 2026.

https://arxiv.org/abs/2606.00286

Also: noise, disorder, disorder & fluctuations, random, intermittency, escape, particle, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, noise, disorder, disorder & fluctuations, randomness, intermittency, escape, particles, quenched disorder, transport dynamics, diffusive and processive transport, arrays of filaments, random walk, random filament networks, escape from local traps.

# gst: describing a universal critical behavior in a transition from order to chaos.

<< ️(AA) present a comprehensive discussion of a transition from integrability to nonintegrability in an oval billiard with a static boundary. This transition is controlled by a deformation parameter 𝜀, which modifies the boundary shape from circular, corresponding to 𝜀=0 and an integrable dynamics, to oval for 𝜀≠0, where nonintegrability emerges. >>

<< ️The deformation of the circular billiard gives rise to a chaotic layer that develops along a well-defined stripe in phase space. By introducing a set of transformations that isolate this chaotic stripe, (They) characterize the diffusive spreading of ensembles of trajectories and identify an observable, 𝜔_(rms,sat), which plays the role of an order parameter for the transition. >>

<< For small deformations, the saturation value of the diffusion obeys the scaling law 𝜔_(rms,sat)∝𝜀^(˜𝛼), with a critical exponent ˜𝛼=0.507⁢(2), vanishing continuously as 𝜀→0. The associated susceptibility, 𝜒=𝑑⁢𝜔_(rms,sat)/𝑑⁢𝜀, diverges in the same limit, signaling the presence of critical behavior analogous to that observed in second-order (continuous) phase transitions in statistical mechanics. >>

Edson D. Leonel, Mayla A. M. de Almeida, Juan Pedro Tarigo, et al. Describing a universal critical behavior in a transition from order to chaos. Phys. Rev. E 113, 054220. May 28, 2026.

https://journals.aps.org/pre/abstract/10.1103/7231-j7zv

arXiv: 2602.17810v1 [nlin.CD]. Feb 19, 2026.

https://arxiv.org/abs/2602.17810

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

Keywords: gst, billiard, oval billiard, transitions, order, disorder, elementary excitations, small deformations, topological defects, criticality, chaotic stripes, chaos.

# gst: evolving fractal dimensions in iterative bicolored percolation.

<< ️Criticality is traditionally regarded as an unstable, fine-tuned fixed point of the renormalization group. (AA)  introduce an iterative bicolored percolation process in two dimensions and show that it can both preserve criticality and transform fractal dimensions. >>

<< ️Starting from critical configurations, such as the O⁡(𝑛) loop and fuzzy Potts models, successive coarse graining generates a hierarchy of distinct yet critical generations. Using the conformal loop ensemble, (They) derive exact, generation-dependent fractal dimensions, which are quantitatively confirmed by large-scale Monte Carlo simulations. The evolutionary trajectory depends not only on the universality class of the initial state but also on whether it possesses a two-state critical structure, leading to different critical exponents starting from site and bond percolation. >>

<< ️These results establish a general geometric mechanism for evolving fractal dimensions, in which scale invariance persists across generations. >>

Shuo Wei, Haoyu Liu, Xin Sun, et al. Evolving fractal dimensions in iterative bicolored percolation. Phys. Rev. E 113, L032102. Mar 23, 2026.

https://journals.aps.org/pre/abstract/10.1103/s2ql-zxz6#4eafda38-c97e-4656-8034-9a3682fa0218

arXiv: 2511.18462v2 [cond-mat.stat-mech]. Mar 24, 2026. 

https://arxiv.org/abs/2511.18462

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

Keywords: gst, order, disorder, fluctuations, percolation, fractal dimensions, criticality, coarse-graining transformations.

# gst: entropy production rate in stochastically time-evolving asymmetric networks.

<< ️Fluctuations in parameters that are typically treated as fixed play a crucial role in the behavior of complex systems. However, to date, we lack a general non-equilibrium thermodynamic treatment of such a complex system. In this Letter, to address this problem, (AA) develop a framework in which fluctuating interactions between units of nonlinear network systems are modeled as uncorrelated colored noise (i.e., annealed disorder) with a correlation time. >>

<< ️This approach enables us to quantify how the entropy production rate (EPR) depends on both the characteristic time-scale and the strength of the disorder. Using dynamical mean field theory, (They) derive an exact expression for EPR at any transient time that is validated by simulations of the full non-linear dynamics. At stationarity, a relation between EPR and autocorrelation is established and then used to analytically study the particular case of linear systems. >>

Tuan Pham, Deepak Gupta. Entropy Production Rate in Stochastically Time-evolving Asymmetric Networks. arXiv: 2603.27658v1 [cond-mat.stat-mech]. Mar 29, 2026.

https://arxiv.org/abs/2603.27658

Also: network, noise, order, disorder, fluctuations, entropy, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, network, entropy, noise, order, disorder, fluctuations.

# gst: spatiotemporal noise stabilizes unbounded diversity in strongly-competitive communities.

<< ️Classical ecological models predict that large, diverse communities should be unstable, presenting a central challenge to explaining the stable biodiversity seen in nature. (AA) revisit this long-standing problem by extending the generalized Lotka-Volterra model to include both spatial structure and environmental fluctuations across space and time.  >>

<< ️(They) find that neither space nor environmental noise alone can resolve the tension between diversity and stability, but that their combined effects permit arbitrarily many species to stably coexist despite strongly disordered competitive interactions. (They) analytically characterize the noise-induced transition to coexistence, showing that spatiotemporal noise drives an anomalous scaling of abundance fluctuations, known empirically as Taylor's law. >>

<< ️At the community level, this manifests as an effective sublinear self-inhibition that renders the community stable and asymptotically neutral in the high-diversity limit. Spatiotemporal noise thus provides a novel resolution to the diversity-stability paradox and a generic mechanism by which complex communities can persist. >>

Amer Al-Hiyasat, Daniel W. Swartz, Jeff Gore, et al. Spatiotemporal noise stabilizes unbounded diversity in strongly-competitive communities. arXiv: 2602.13423v1 [q-bio.PE]. Feb 13, 2026.

https://arxiv.org/abs/2602.13423

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

Keywords: gst, noise, spatiotemporal noise, disorder, transition, noise-induced transition, disordered competitive interactions, spatial structure and environmental fluctuations.

# gst: steady states in a model of opposing local and nonlocal hops.

<< ️(AA) study a one-dimensional lattice model of particles following hard-core exclusion and performing opposing local and nonlocal moves with probability 𝑝 and 1−𝑝, respectively. (Their) model shows the interesting feature that the direction of the particle current can be switched by simply changing the density 𝜌 of particles on the lattice. (They) study the dependence of current on 𝑝 as well as 𝜌 and present the separation of positive and negative current regions on a 𝑝−𝜌 plane. >>

<< ️Further, (They) study the effect of disorder on this model by introducing a single site with valvelike dynamics. The site allows only unidirectional, local outward motion with rate 𝑟. The interplay of the disorder strength 𝑟, particle density 𝜌, and probability 𝑝 leads to a rich possibility with four different kinds of shock phases in the steady state. >>

<< ️(They) study the shock densities using Monte Carlo simulations and mean field calculations. While (Their) mean field treatment describes the numerical results quite well qualitatively, (AA) see certain quantitative deviations. (They) try to understand these deviations using measures of correlation in the system and provide heuristic arguments for the mismatch. >>

Ankur Mishra, Apoorva Nagar. Steady states in a model of opposing local and nonlocal hops. Phys. Rev. E 113, 024113. Feb 10, 2026.

https://journals.aps.org/pre/abstract/10.1103/66lp-n7hv

Also: particle, disorder, transitions, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particles, disorder, phase transitions, shock phases, valvelike dynamics.

# gst: spatial self-organization driven by temporal noise.

<< ️The counterintuitive emergence of order from noise is a central phenomenon in science, ranging from pattern formation and synchronization to order-by-disorder in frustrated systems. While large-scale spatial self-organization induced by local spatial noise is well studied, whether temporal noise can also drive such organization remains an open question. >>

<< ️Here, by studying interacting particle systems, (AA) show that temporally correlated noise can lead to a self-organized state with suppressed long-range density fluctuations, or hyperuniformity. Further, (They) develop a fluctuating hydrodynamic theory that quantitatively explains the origin of this phenomenon. >>

<< ️Finally, by casting the dynamics as a stochastic optimization problem, (They) show that temporal correlations lead to better solutions, akin to perturbed gradient descent in neural networks -- where noise is injected during training to escape poor minima. This reveals a striking correspondence between perturbed gradient descent dynamics on the energy landscapes of particle systems and the loss landscapes of neural networks. >>

Satyam Anand, Guanming Zhang, Stefano Martiniani. Spatial self-organization driven by temporal noise. arXiv: 2601.23098v1 [cond-mat.soft]. Jan 30, 2026.

https://arxiv.org/abs/2601.23098

Also: self-assembly, noise, order, disorder, disorder & fluctuations, particle, escape, network, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, self-assembly, noise, order, disorder, disorder & fluctuations, particles, networks, neural networks, spatial noise, temporal noise, noise-driven self-organization.

# gst: nonlocal Kramers-Moyal formulas and data-driven discovery of stochastic dynamical systems with multiplicative Lévy noise.

<< ️Traditional data-driven methods, effective for deterministic systems or stochastic differential equations (SDEs) with Gaussian noise, fail to handle the discontinuous sample paths and heavy-tailed fluctuations characteristic of Lévy processes, particularly when the noise is state-dependent. >>

<< ️To bridge this gap, (AA) establish nonlocal Kramers-Moyal formulas, rigorously generalizing the classical Kramers-Moyal relations to SDEs with multiplicative Lévy noise. These formulas provide a direct link between short-time transition probability densities (or sample path statistics) and the underlying SDE coefficients: the drift vector, diffusion matrix, Lévy jump measure kernel, and Lévy noise intensity functions. >>

<< This (AA) work provides a principled and practical toolbox for discovering interpretable SDE models governing complex systems influenced by discontinuous, heavy-tailed, state-dependent fluctuations, with broad applicability in climate science, neuroscience, epidemiology, finance, and biological physics. >>

Yang Li, Jinqiao Duan. Nonlocal Kramers-Moyal formulas and data-driven discovery of stochastic dynamical systems with multiplicative Lévy noise. arXiv: 2601.19223v1 [math.DS]. Jan 27, 2026.

https://arxiv.org/abs/2601.19223

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

Keywords: gst, noise, randomness, transitions, fluctuations.

# gst: quantum avalanche stability of many-body localization with power-law interactions.

<< ️(AA) investigate the stability of the many-body localized (MBL) phase against quantum avalanche instabilities in a one-dimensional Heisenberg spin chain with long-range power-law interactions (V ∝ r−α). >>

<< ️(They) finite-size scaling analysis of entanglement entropy identifies a critical interaction exponent αc ≈ 2, which separates a fragile regime, characterized by an exponentially diverging critical disorder, from a robust short-range regime. >>

<< ️(AA) results confirm that the MBL phase remains asymptotically stable in the thermodynamic limit when disorder exceeds an interaction-dependent threshold. >>

Longhui Shen, Bin Guo, Zhaoyu Sun. Quantum Avalanche Stability of Many-Body Localization with Power-Law Interactions. arXiv: 2601.13485v1 [cond-mat.dis-nn]. Jan 20, 2026.

https://arxiv.org/abs/2601.13485

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

Keywords: gst, disorder, avalanche, avalanche stability, entanglement entropy, criticality. 

# gst: generation of disordered networks with targeted structural properties.

<< ️Disordered spatial networks are model systems that describe structures and interactions across multiple length scales. Scattering and interference of waves in these networks can give rise to structural phase transitions, localization, diffusion, and band gaps. >>

<< ️(AA) tune the degree and type of disorder introduced into initially crystalline networks by varying the bond-bending force constant in the strain energy and the temperature profile. >>

<< ️As a case study, (AA) statistically reproduce four disordered biophotonic networks exhibiting structural color. This work presents a versatile method for generating disordered networks with tailored structural properties. It will enable new insights into structure-property relations, such as photonic band gaps in disordered networks. >>

Florin Hemmann, Vincent Glauser, Ullrich Steiner, Matthias Saba. Computer Generation of Disordered Networks with Targeted Structural Properties. arXiv: 2601.10333v1 [cond-mat.dis-nn]. Jan 15, 2026.

https://arxiv.org/abs/2601.10333

Also: network, waves, disorder, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, disorder, disordered networks, waves, phase transitions.