# 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. 

# brain: spontaneous emergence of metacognition in neuronal computation.

<< ️Metacognition, a hallmark of human intelligence, enables individuals to assess prediction uncertainty, providing an advantage over artificial intelligence in anticipating risks and performing tasks that demand trustworthiness and reliability. >>

<< ️Here, (AA) demonstrate that metacognition can naturally emerge in recurrent neural networks trained on cognitive tasks without guidance from any probabilistic inference rules or additional network architectures. Through naturally embedded nonlinear coupling with the mean of the network output, the covariance of the network output engages in metacognition by assessing the uncertainty associated with the mean, which represents the task responses. >>

<< ️(AA) further propose testable predictions about how key features of neuronal computation in the brain—noise, neuronal correlations, and heterogeneity—contribute to metacognition. >>

Hengyuan Ma, Wenlian Lu, Jianfeng Feng. Spontaneous emergence of metacognition in neuronal computation. Phys. Rev. Research 7, 033188. Aug 22, 2025.

https://journals.aps.org/prresearch/abstract/10.1103/f1hv-bf1f

Also: brain, network, uncertainty, noise, chaos, in  https://www.inkgmr.net/kwrds.html 

Keywords: gst, brain, cognition, metacognition, learning, memory, networks, biological neural networks, biological information processing, decision making, uncertainty, stochasticity, noise, chaos.

# 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.

# life: self-reinforcing cascades: a spreading model for beliefs or products of varying intensity or quality

<< ️Models of how things spread often assume that transmission mechanisms are fixed over time. However, social contagions—the spread of ideas, beliefs, innovations—can lose or gain in momentum as they spread: ideas can get reinforced, beliefs strengthened, products refined. >>

<< ️(AA) study the impacts of such self-reinforcement mechanisms in cascade dynamics. (They) use different mathematical modeling techniques to capture the recursive, yet changing nature of the process. >>

<< ️(AA) find a critical regime with a range of power-law cascade size distributions with nonuniversal scaling exponents. This regime clashes with classic models, where criticality requires fine-tuning at a precise critical point. Self-reinforced cascades produce critical-like behavior over a wide range of parameters, which may help explain the ubiquity of power-law distributions in empirical social data. >>

Laurent Hébert-Dufresne, Juniper Lovato, et al. Self-Reinforcing Cascades: A Spreading Model for Beliefs or Products of Varying Intensity or Quality. Phys. Rev. Lett. 135, 087401. Aug 21, 2025.

https://journals.aps.org/prl/abstract/10.1103/5mph-sws5

Also: behav, random, noise, walk, self-assembly, in https://www.inkgmr.net/kwrds.html 

Keywords: life, behavior, walk, random, random walks, noise, criticality, self-assembly, social contagions, self-reinforced cascades.

# gst: apropos of instabilities, stability of co-annular active and passive confined fluids.

<< ️The translation and shape deformations of a passive viscous Newtonian droplet immersed in an active nematic liquid crystal under circular confinement are analyzed using a linear stability analysis. (AA) focus on the case of a sharply aligned active nematic in the limit of strong elastic relaxation in two dimensions. >>

<< ️Using an active liquid crystal model, (They) employ the Lorentz reciprocal theorem for Stokes flow to study the growth of interfacial perturbations as a result of both active and elastic stresses. >>

<< ️Instabilities are uncovered in both extensile and contractile systems, for which growth rates are calculated and presented in terms of the dimensionless ratios of active, elastic, and capillary stresses, as well as the viscosity ratio between the two fluids. >>

<< ️(AA) also extend (Their) theory to analyze the inverse scenario, namely, the stability of an active nematic droplet surrounded by a passive viscous layer. (Their) results highlight the subtle interplay of capillary, active, elastic, and viscous stresses in governing droplet stability. >>

<< ️The instabilities uncovered here may be relevant to a plethora of biological active systems, from the dynamics of passive droplets in bacterial suspensions to the organization of subcellular compartments inside the cell and the cell nucleus. >>

Tanumoy Dhar, Michael J. Shelley, David Saintillan. Stability of co-annular active and passive confined fluids. Phys. Rev. Fluids 10, 083103. Aug 21, 2025.

https://journals.aps.org/prfluids/abstract/10.1103/m5ck-v2q3

arXiv: 2501.04918v2 [cond-mat.soft]. Jul 25, 2025. 

https://arxiv.org/abs/2501.04918

Also: drop, droplet, droploid, elastic, instability, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, drop, droplet, droploid, elasticity, instability, elastic relaxation, interfacial perturbations, capillary, active, elastic, and viscous stresses.

# gst: stationary-state dynamics of interacting phase oscillators in presence of noise and stochastic resetting

<< ️(AA) explore the impact of global resetting on Kuramoto-type models of coupled limit-cycle oscillators with distributed frequencies both in absence and presence of noise. The dynamics comprises repeated interruption of the bare dynamics at random times with simultaneous resetting of phases of all the oscillators to a predefined state. >>

<< ️A key finding is the pivotal role of correlations in shaping the ordering dynamics under resettling. >>

<< ️It would be interesting to consider suitable refinement to the mean-field approximation  invoked in this work in order to have a better match of analytical with simulation results. An immediate extension is to consider resetting only a subset of the degrees of freedom at random times. >>

Anish Acharya, Mrinal Sarkar, Shamik Gupta. Stationary-state dynamics of interacting phase oscillators in presence of noise and stochastic resetting. arXiv: 2504.08510v2 [cond-mat.stat-mech].  https://arxiv.org/abs/2504.08510v2

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

Keywords: gst, coupled limit-cycle oscillators, stationary-state behavior, global resetting, quenched disorder, annealed disorder, random times, noise.

# 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