Fluctuation loops in noise-driven linear dynamical systems

Ghanta, Akhil; Neu, John C.; Teitsworth, Stephen W.

doi:10.1103/physreve.95.032128

Cited by 33 publications

(49 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For Eq. (E2), the stochastic area swept by the particle in the x-v plane increases linearly with time, which indicates nonequilibrium [18]. In fact, the time average of the stochastic area is A = lim t→∞ 1 2t t 0 (vẋ − xv) dt = (LM + D) 12 = xv = (1 + k) −1 = 0.…”

Section: (E8)mentioning

confidence: 99%

Active Ornstein-Uhlenbeck particles

Bonilla

2019

Phys. Rev. E

View full text Add to dashboard Cite

Active Ornstein-Uhlenbeck particles (AOUPs) are overdamped particles in an interaction potential subject to external Ornstein-Uhlenbeck noises. They can be transformed into a system of underdamped particles under additional velocity dependent forces and subject to white noise forces. There has been some discussion in the literature on whether AOUPs can be in equilibrium for particular interaction potentials and how far from equilibrium they are in the limit of small persistence time. By using a theorem on the time reversed form of the AOUP Langevin-Ito equations, I prove that they have an equilibrium probability density invariant under time reversal if and only if their smooth interaction potential has zero third derivatives. In the limit of small persistence Ornstein-Uhlenbeck time τ , a Chapman-Enskog expansion of the Fokker-Planck equation shows that the probability density has a local equilibrium solution in the particle momenta modulated by a reduced probability density that varies slowly with the position. The reduced probability density satisfies a continuity equation in which the probability current has an asymptotic expansion in powers of τ . Keeping up to O(τ ) terms, this equation is a diffusion equation, which has an equilibrium stationary solution with zero current. However, O(τ 2 ) terms contain fifth and sixth order spatial derivatives and the continuity equation no longer has a zero current stationary solution. The expansion of the overall stationary solution now contains odd terms in the momenta, which clearly shows that it is not an equilibrium.

show abstract

Section: (E8)mentioning

confidence: 99%

Active Ornstein-Uhlenbeck particles

Bonilla

2019

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…It is well-known that systems in thermodynamic equilibrium obey detailed balance which requires that transition rates between any two microscopic states are pairwise balanced [23]. For non-equilibrium steady state situations, however, detailed balance is broken and a probability flux loop should exist in a configurational phase space [24][25][26][27]. Such a probability flux has been experimentally measured in the periodic beating of a flagellum from Chlamydomonas reinhardtii and in the non-periodic fluctuations of primary cilia of epithelial cells [28].…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium probability flux of a thermally driven micromachine

et al. 2019

View full text Add to dashboard Cite

We discuss the non-equilibrium statistical mechanics of a thermally driven micromachine consisting of three spheres and two harmonic springs [Y. Hosaka et al., J. Phys. Soc. Jpn. 86 (2017)]. We obtain the non-equilibrium steady state probability distribution function of such a micromachine and calculate its probability flux in the corresponding mode space. The resulting probability flux can be expressed in terms of a frequency matrix that is used to distinguish between a non-equilibrium steady state and a thermal equilibrium state satisfying detailed balance. We analytically show that the probability flux of a micromachine is proportional to the temperature difference between the first and the third spheres when the friction coefficients are all identical. The scale of non-equilibrium of a micromachine can quantitatively be characterized by the flux rotor. We obtain a linear relation between the flux rotor and the average velocity of a thermally driven micromachine that can undergo a directed motion in a viscous fluid.

show abstract

“…Broken detailed balance can be determined from circulating currents in the coordinates space of pairs of mesoscopic degrees of freedom. Frequently used measures to quantify circulating currents in phase space are the area enclosing rate and the cycling frequency of the stochastic trajectories [25,33,34]. These measures are closely related to the entropy production rate [27,28].…”

Section: Introductionmentioning

confidence: 99%

Mesoscopic non-equilibrium measures can reveal intrinsic features of the active driving

2019

View full text Add to dashboard Cite

Biological assemblies such as chromosomes, membranes, and the cytoskeleton are driven out of equilibrium at the nanoscale by enzymatic activity and molecular motors. Similar non-equilibrium dynamics can be realized in synthetic systems, such as chemically fueled colloidal particles. Characterizing the stochastic non-equilibrium dynamics of such active soft assemblies still remains a challenge. Recently, new non-invasive approaches have been proposed to determine non-equilibrium behavior, which are based on detecting broken detailed balance in the stochastic trajectories of several coordinates of the system. Inspired by the method of two-point microrheology, in which the equilibrium fluctuations of a pair of probe particles reveal the viscoelastic response of an equilibrium system, here we investigate whether we can extend such an approach to non-equilibrium assemblies: can one extract information on the nature of the active driving in a system from the analysis of a two-point non-equilibrium measure? We address this question theoretically in the context of a class of elastic systems, driven out of equilibrium by a spatially heterogeneous stochastic internal driving. We consider several scenarios for the spatial features of the internal driving that may be relevant in biological and synthetic systems, and investigate how such features of the active noise may be reflected in the long-range scaling behavior of two-point non-equilibrium measures.

show abstract

Fluctuation loops in noise-driven linear dynamical systems

Cited by 33 publications

References 22 publications

Active Ornstein-Uhlenbeck particles

Active Ornstein-Uhlenbeck particles

Nonequilibrium probability flux of a thermally driven micromachine

Mesoscopic non-equilibrium measures can reveal intrinsic features of the active driving

Contact Info

Product

Resources

About