Noise-Induced Drift in Stochastic Differential Equations with Arbitrary Friction and Diffusion in the Smoluchowski-Kramers Limit

Hottovy, Scott; Volpe, Giovanni; Wehr, Jan

doi:10.1007/s10955-012-0418-9

Cited by 58 publications

(63 citation statements)

References 27 publications

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“…The main aim is to understand how the stochastic thermodynamics is affected by "coarsegraining" the level of description of the particle motion when performing the overdamped limit to "integrate out" the fast velocity degrees of freedom. This question is of particular interest in case that the surrounding heat bath is heterogeneous, a situation which is known to be non-trivial already for the particle's equations of motion [41][42][43][44][45][46][47][48]. A central quantity for such an analysis is the trajectory-wise entropy production of the particle defined according to stochastic thermodynamics [16].…”

Section: Discussionmentioning

confidence: 99%

Entropy production of a Brownian ellipsoid in the overdamped limit

2016

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We analyze the translational and rotational motion of an ellipsoidal Brownian particle from the viewpoint of stochastic thermodynamics. The particle's Brownian motion is driven by external forces and torques and takes place in an heterogeneous thermal environment where friction coefficients and (local) temperature depend on space and time. Our analysis of the particle's stochastic thermodynamics is based on the entropy production associated with single particle trajectories. It is motivated by the recent discovery that the overdamped limit of vanishing inertia effects (as compared to viscous fricion) produces a so-called "anomalous" contribution to the entropy production, which has no counterpart in the overdamped approximation, when inertia effects are simply discarded. Here, we show that rotational Brownian motion in the overdamped limit generates an additional contribution to the "anomalous" entropy. We calculate its specific form by performing a systematic singular perturbation analysis for the generating function of the entropy production. As a side result, we also obtain the (well-known) equations of motion in the overdamped limit. We furthermore investigate the effects of particle shape and give explicit expressions of the "anomalous entropy" for prolate and oblate spheroids and for near-spherical Brownian particles.

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Section: Discussionmentioning

confidence: 99%

Entropy production of a Brownian ellipsoid in the overdamped limit

2016

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“…Generally, the Itô interpretation is employed in economics and biology due to their features of being 'only related to the latest past'; the Stratonovich integral finds applications in physical systems, such as electrical circuits driven by multiplicative noises (see [51], and references therein). In particular, it finds that with decreasing the mass of particles a second-order Langevin equation can reduce to a first-order one with different noise-induced drifts, depending on the relationship between friction and diffusion coefficients [51][52][53]. For example, a second-order Langevin system with a constant friction coefficient but a position-dependent diffusivity will converge to a first-order equation without noise-induced drift.…”

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confidence: 99%

Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity

Mei

et al. 2020

New J. Phys.

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This work focuses on the dynamics of particles in a confined geometry with position-dependent diffusivity, where the confinement is modelled by a periodic channel consisting of unit cells connected by narrow passage ways. We consider three functional forms for the diffusivity, corresponding to the scenarios of a constant (D 0 ), as well as a low (D m ) and a high (D d ) mobility diffusion in cell centre of the longitudinally symmetric cells. Due to the interaction among the diffusivity, channel shape and external force, the system exhibits complex and interesting phenomena. By calculating the probability density function, mean velocity and mean first exit time with the Itô calculus form, we find that in the absence of external forces the diffusivity D d will redistribute particles near the channel wall, while the diffusivity D m will trap them near the cell centre. The superposition of external forces will break their static distributions. Besides, our results demonstrate that for the diffusivity D d , a high dependence on the x coordinate (parallel with the central channel line) will improve the mean velocity of the particles. In contrast, for the diffusivity D m , a weak dependence on the x coordinate will dramatically accelerate the moving speed. In addition, it shows that a large external force can weaken the influences of different diffusivities; inversely, for a small external force, the types of diffusivity affect significantly the particle dynamics. In practice, one can apply these results to achieve a prominent enhancement of the particle transport in two-or three-dimensional channels by modulating the local tracer diffusivity via an engineered gel of varying porosity or by adding a cold tube to cool down the diffusivity along the central line, which may be a relevant effect in engineering applications. Effects of different stochastic calculi in the evaluation of the underlying multiplicative stochastic equation for different physical scenarios are discussed.New J. Phys. 22 (2020) 053016 Y Li et al confined spaces, transport of particles in nanopores, zeolites and gel networks [8-10], or protein diffusion in the mammalian cell cytoplasm [11]. In many cases, such structured environments can be viewed as confined channels with different boundaries and properties [12][13][14]. The behaviours of systems in these confined channels have been studied by virtue of the analytical Fick-Jacobs (FJ) equation and numerical simulations of the dynamic equations [15][16][17][18][19][20]. Results for symmetric periodic channels indicate that the mean transport velocity may be proportional to large external forces in the confined environment [19][20][21][22]. For asymmetric channels, it was found that the shape of the confinement contributes to the moving direction and mean displacement [20,23], which can be applied to fine separation of mixtures and also the design of many devices [24,25]. Time-dependent and deformable boundaries were discussed to explore the activity in living cells [26,27]. In addition, the interaction...

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“…If desired, one can change the convention, but only by adding an appropriate drift term at the same time. We emphasize that in the present article the coefficients of the equation do not change; it would also be possible to keep the Itô convention throughout and change the drift term accordingly as a varies 16 . Various preferences regarding the appropriate choice of a have emerged in various fields in which SDEs have been fruitfully applied.…”

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Stratonovich-to-Itô transition in noisy systems with multiplicative feedback

et al. 2013

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Intrinsically noisy mechanisms drive most physical, biological and economic phenomena. Frequently, the system's state influences the driving noise intensity (multiplicative feedback). These phenomena are often modelled using stochastic differential equations, which can be interpreted according to various conventions (for example, Itô calculus and Stratonovich calculus), leading to qualitatively different solutions. Thus, a stochastic differential equationconvention pair must be determined from the available experimental data before being able to predict the system's behaviour under new conditions. Here we experimentally demonstrate that the convention for a given system may vary with the operational conditions: we show that a noisy electric circuit shifts from obeying Stratonovich calculus to obeying Itô calculus. We track such a transition to the underlying dynamics of the system and, in particular, to the ratio between the driving noise correlation time and the feedback delay time. We discuss possible implications of our conclusions, supported by numerics, for biology and economics.

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Noise-Induced Drift in Stochastic Differential Equations with Arbitrary Friction and Diffusion in the Smoluchowski-Kramers Limit

Cited by 58 publications

References 27 publications

Entropy production of a Brownian ellipsoid in the overdamped limit

Entropy production of a Brownian ellipsoid in the overdamped limit

Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity

Stratonovich-to-Itô transition in noisy systems with multiplicative feedback

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