Equilibrium stochastic delay processes

Holubec, Viktor; Ryabov, Artem; Loos, Sarah A. M.; Kroy, Klaus

doi:10.1088/1367-2630/ac4b91

Cited by 4 publications

(3 citation statements)

References 88 publications

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“…Unfortunately, SDDEs are notoriously difficult for analytical treatment if they are not linear [28,29]. SDDEs with nonlinear forces can generally only be treated approximately, using a linearization, small or large delay approxiamation [30] or by expansions around an equilibrium dynamics [31]. Therefore, the main tools for studying SDDEs are numerical methods.…”

Section: Introductionmentioning

confidence: 99%

Matrix numerical method for probability densities of stochastic delay differential equations

Antary,

Holubec

2024

J. Phys. A: Math. Theor.

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Stochastic processes with time delay are invaluable for modeling in science and engineering when finite signal transmission and processing speeds can not be neglected. However, they can seldom be treated with sufficient precision analytically if the corresponding stochastic delay differential equations (SDDEs) are nonlinear. This work presents a numerical algorithm for calculating the probability densities of processes described by nonlinear SDDEs. The algorithm is based on Markovian embedding and solves the problem by basic matrix operations. We validate it for a broad class of parameters using exactly solvable linear SDDEs and a cubic SDDE. Besides, we show how to apply the algorithm to calculate transition rates and first passage times for a Brownian particle diffusing in a time-delayed cusp potential.

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Section: Introductionmentioning

confidence: 99%

Matrix numerical method for probability densities of stochastic delay differential equations

Antary,

Holubec

2024

J. Phys. A: Math. Theor.

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“…The system is therefore in thermal equilibrium and the equipartition theorem is fulfilled, ⟨v i (0)v j (0)⟩ = k B Tδ ij . • FEED: The non-equilibrium system FEED is characterized by specific non-reciprocal interactions such that the memory kernel has a maximum at time t > 0, and thus resembles a time-delay feedback mechanism [40][41][42][43]. The parameters of the system are k…”

Section: The Microscopic Modelmentioning

confidence: 99%

“…The main objective of this work is therefore to better understand how dynamic coarsegraining techniques can be used to analyze non-equilibrium phenomena and to better analyze transport properties of the reconstructed coarse-grained models. Our analysis is based on an analytically solvable non-equilibrium system [35,40], which, depending on the chosen parameters, can resemble systems featuring time-delayed feedback [40][41][42][43] or active Ornstein-Uhlenback particles [44]. Using this system we have recently highlighted that although the Mori-Zwanzig (MZ) formalism [6,26,27,[45][46][47] suggests the existence of a 2FDT via the projection operator formalism, the exactly derivable GLE clearly proves that the 2FDT is violated [36].…”

Section: Introductionmentioning

confidence: 99%

Mobility, response and transport in non-equilibrium coarse-grained models

Jung

2024

J. Phys. A: Math. Theor.

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We investigate two diﬀerent types of non-Markovian coarse-grained models extracted from a linear, non-equilibrium microscopic system, featuring a tagged particle coupled to underdamped oscillators. The ﬁrst model is obtained by analytically “integrating out” the oscillators and the second is based on a derivation using projection operator techniques. We observe that these two models behave very diﬀerently when the tagged particle is exposed to external harmonic potentials or pulling forces. Most importantly, we ﬁnd that the analytic model has a well deﬁned friction kernel and can be used to extract work, consistent with the microscopic system, while the projection model corresponds to an eﬀective equilibrium model, which cannot be used to extract work. We apply the analysis to two popular non-equilibrium systems, time-delay feedback control and the active Ornstein-Uhlenbeck process. Finally, we highlight that our study could have important consequences for dynamic coarse-graining of non-equilibrium systems going far beyond the linear systems investigated in this manuscript.

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Feedback-controlled solute transport through chemo-responsive polymer membranes

Milster

Kim

Dzubiella

2023

The Journal of Chemical Physics

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Polymer membranes are typically assumed to be inert and nonresponsive to the flux and density of the permeating particles in transport processes. Here, we study theoretically the consequences of membrane responsiveness and feedback on the steady-state force-flux relations and membrane permeability using a nonlinear-feedback solution-diffusion model of transport through a slab-like membrane. Therein, the solute concentration inside the membrane depends on the bulk concentration, c0, the driving force, f, and the polymer volume fraction, φ. In our model, solute accumulation in the membrane causes a sigmoidal volume phase transition of the polymer, changing its permeability, which, in return, affects the membrane's solute uptake. This feedback leads to nonlinear force-flux relations, j(f), which we quantify in terms of the system's differential permeability, PΔsys∝d j/d f. We find that the membrane feedback can increase or decrease the solute flux by orders of magnitude, triggered by a small change in the driving force, and largely tunable by attractive versus repulsive solute-membrane interactions. Moreover, controlling the input, c0 and f, can lead to steady-state bistability of φ and hysteresis in the force-flux relations. This work advocates that the fine-tuning of the membrane's chemo-responsiveness will enhance the nonlinear transport control features, providing great potential for future (self-)regulating membrane devices.

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Equilibrium stochastic delay processes

Cited by 4 publications

References 88 publications

Matrix numerical method for probability densities of stochastic delay differential equations

Matrix numerical method for probability densities of stochastic delay differential equations

Mobility, response and transport in non-equilibrium coarse-grained models

Feedback-controlled solute transport through chemo-responsive polymer membranes

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