Path Integrals for Stochastic Processes

Wio, Horacio S.

doi:10.1142/8695

Cited by 85 publications

(140 citation statements)

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“…where b = βDmω ‡ 2 is the frequency involved in overdamped motion. To describe the probability functional for a Brownian path one has the Onsager-Marchlup Lagragian associated with the Brownian motion in the inverted harmonic potential 29 :…”

Section: Harmonic Barriermentioning

confidence: 99%

On the hydrodynamics of swimming enzymes

Bai

Wolynes

2015

The Journal of Chemical Physics

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Several recent experiments suggest that rather generally the diffusion of enzymes may be augmented through their activity. We demonstrate that such swimming motility can emerge from the interplay between the enzyme energy landscape and the hydrodynamic coupling of the enzyme to its environment. Swimming thus occurs during the transit time of a transient allosteric change. We estimate the velocity during the transition. The analysis of such a swimming motion suggests the final stroke size is limited by the hydrodynamic size of the enzyme. This limit is quite a bit smaller than the values that can be inferred from the recent experiments. We also show that one proposed explanation of the experiments based on reaction heat effects can be ruled out using an extended hydrodynamic analysis. These results lead us to propose an alternate explanation of the fluorescence correlation measurements.

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Section: Harmonic Barriermentioning

confidence: 99%

On the hydrodynamics of swimming enzymes

Bai

Wolynes

2015

The Journal of Chemical Physics

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“…Here we introduce the pre-point discretization procedure of the path integral according to Refs. [24,25]. We focus on the one-dimensional case because the calculations for the multi-dimensional case is laborious.…”

Section: Discussionmentioning

confidence: 99%

“…(5) Let P θ (Γ|x 0 ) be the probability of Γ given x 0 at t = 0. By using a path integral [14,[23][24][25], we obtain (Appendix B)…”

Section: Modelmentioning

confidence: 99%

Uncertainty relations in stochastic processes: An information inequality approach

Hasegawa

2019

Phys. Rev. E

117

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The thermodynamic uncertainty relation is an inequality stating that it is impossible to attain higher precision than the bound defined by entropy production. In statistical inference theory, information inequalities assert that it is infeasible for any estimator to achieve an error smaller than the prescribed bound. Inspired by the similarity between the thermodynamic uncertainty relation and the information inequalities, we apply the latter to systems described by Langevin equations and derive the bound for the fluctuation of thermodynamic quantities. When applying the Cramér-Rao inequality, the obtained inequality reduces to the fluctuation-response inequality. We find that the thermodynamic uncertainty relation is a particular case of the Cramér-Rao inequality, in which the Fisher information is the total entropy production. Using the equality condition of the Cramér-Rao inequality, we find that the stochastic total entropy production is the only quantity which can attain equality in the thermodynamic uncertainty relation. Furthermore, we apply the Chapman-Robbins inequality and obtain a relation for the lower bound of the ratio between the variance and the sensitivity of systems in response to arbitrary perturbations.

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“…This depends on the underlying discretization of the coordinates, and may need to be modified if higher order corrections to the rate are computed. Here only the leading non-perturbative contribution is considered, and the Jacobian is irrelevant18). The integral over x and t in Eq.…”

Section: Derivation Of Exact Ratementioning

confidence: 99%

Kink pair production and dislocation motion

Fitzgerald

2016

Sci Rep

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The motion of extended defects called dislocations controls the mechanical properties of crystalline materials such as strength and ductility. Under moderate applied loads, this motion proceeds via the thermal nucleation of kink pairs. The nucleation rate is known to be a highly nonlinear function of the applied load, and its calculation has long been a theoretical challenge. In this article, a stochastic path integral approach is used to derive a simple, general, and exact formula for the rate. The predictions are in excellent agreement with experimental and computational investigations, and unambiguously explain the origin of the observed extreme nonlinearity. The results can also be applied to other systems modelled by an elastic string interacting with a periodic potential, such as Josephson junctions in superconductors.

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Path Integrals for Stochastic Processes

Cited by 85 publications

References 0 publications

On the hydrodynamics of swimming enzymes

On the hydrodynamics of swimming enzymes

Uncertainty relations in stochastic processes: An information inequality approach

Kink pair production and dislocation motion

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