# gst: stochastic Scovil-Schulz-DuBois (SSDB) machine and its three types of cycles

<< Three types of cycles are identified in the quantum jump trajectories of the Scovil–Schulz-DuBois (SSDB) machine. An R cycle as refrigeration, an H cycle as a heat engine, and an N cycle in which the machine is neutral. >>

AA << find that in the large time limit, whether the machine operates as a heat engine or refrigerator depends on the ratio between the numbers of R cycles and H cycles per unit time. Further increasing the hot bath temperature above a certain threshold does not increase the machine's power output. The cause is that, in this situation, the N cycle has a greater probability than the H cycle and R cycle. >>

<< Although the SSDB machine operates by randomly switching between these three cycles, at the level of a single quantum jump trajectory, its heat engine efficiency and the refrigerator's coefficient of performance remain constant. >>

Fei Liu, Jiayin Gu. Stochastic Scovil–Schulz-DuBois machine and its three types of cycles. Phys. Rev. E 111, 014108. Jan 3, 2025. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.111.014108 

arXiv: 2409.04124v2 [cond-mat.stat-mech]. Jan 5, 2025. 

https://arxiv.org/abs/2409.04124

Keywords: gst, stochasticity, quantum heat engines & refrigerators, stochastic Scovil–Schulz-DuBois (SSDB) machine 

# gst: stochastic adaptation, stochastic resonance.

<< Stochastic resonance is a phenomenon possessed by some nonlinear oscillators, in which a weak signal is boosted by noise. Both the monostable and bistable Duffing oscillators can exhibit this property. However, stochastic resonance has a strong frequency-dependence, as only a band of frequencies may be boosted by noise. >>️

<< Adaptive oscillators are a subset of nonlinear oscillators that can learn the features of an external force. (In this AA work), an adaptive state is added to a Duffing oscillator. This adaptive state enables the Duffing adaptive oscillator to outperform stochastic resonance over a wide range of frequencies by learning a resonance condition. >>️

Edmon Perkins. Comparison of stochastic adaptation and stochastic resonance. Phys. Rev. E 110, 064225. Dec 27, 2024.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.110.064225 

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

Keywords: gst, fluctuations, noise, transition, stochasticity, stochastic adaptation, stochastic resonance

# gst: apropos of random walks, intermittent random walks under stochastic resetting

AA << analyze a one-dimensional intermittent random walk on an unbounded domain in the presence of stochastic resetting. In this process, the walker alternates between local intensive search, diffusion, and rapid ballistic relocations in which it does not react to the target. >>

AA << demonstrate that Poissonian resetting leads to the existence of a non-equilibrium steady state. (They) calculate the distribution of the first arrival time to a target along with its mean and show the existence of an optimal reset rate. In particular, (..) the initial condition of the walker, i.e., either starting diffusely or relocating, can significantly affect the long-time properties of the search process. >>

<< the presence of distinct parameter regimes for the global optimization of the mean first arrival time when ballistic and diffusive movements are in direct competition. >>️

Rosa Flaquer-Galmes, Daniel Campos,  Vicenc Mendez. Intermittent random walks under stochastic resetting. Phys. Rev. E 109, 034103. March 4, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.034103  

Also: walk, walking, random, in https://www.inkgmr.net/kwrds.html

Keywords: gst, walk, intermittent random walk, stochasticity, stochastic resetting

# gst: perform statistics of rare events in stochastic processes by defining stochastic bridges from fixed start and end points.

<< The numerical quantification of the statistics of rare events in stochastic processes is a challenging computational problem. (AA) present a sampling method that constructs an ensemble of stochastic trajectories that are constrained to have fixed start and end points (so-called stochastic bridges). (AA) then show that by carefully choosing a set of such bridges and assigning an appropriate statistical weight to each bridge, one can focus more processing power on the rare events of a target stochastic process while faithfully preserving the statistics of these rare trajectories. >>

Javier Aguilar, Joseph W. Baron, et al. 

Sampling rare trajectories using stochastic bridges. Phys. Rev. E 105, 064138. Jun 30, 2022.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.105.064138

Keywords: stochasticity, stochastic processes, stochastic bridges, large deviations, rare trajectories, rare event statistics.

# gst: small-scale random perturbations, Arnold's cat spontaneously stochastic

<< Multi-scale systems (..) may possess a fascinating property of spontaneous stochasticity: a small-scale initial uncertainty develops into a randomly chosen largescale state in a finite time, and this behavior is not sensitive to the nature and magnitude of uncertainty (..). >>

A << intriguing form is the Eulerian spontaneous stochasticity (ESS) of the velocity field itself: an infinitesimal small-scale noise triggers stochastic evolution of velocity field at finite scales and times. >>

AA << prove that a formally deterministic system with scaling symmetry yields a stochastic process with Markovian properties if it is regularized with a vanishing small-scale random perturbation. Besides its significance for understanding turbulence, (their) model extends the phenomenon of ESS beyond the scope of fluid dynamics: (AA) discuss a prototype of a feasible experiment for observing ESS in optics or electronics, as well as potential applications in other physical systems.>>

Alexei A. Mailybaev, Artem Raibekas. Spontaneously stochastic Arnold's cat. arXiv:2111.03666v1 [nlin.CD]. Nov 5,  2021.

https://arxiv.org/abs/2111.03666

keywords: gst, Arnold's cat, randomness, stochasticity, spontaneous stochasticity, small-scale random perturbations, noise, turbulence, chaos