Nonequilibrium Linear Response for Markov Dynamics, I: Jump Processes and Overdamped Diffusions

Baiesi, Marco; Maes, Christian; Wynants, Bram

doi:10.1007/s10955-009-9852-8

Cited by 124 publications

(230 citation statements)

References 48 publications

(149 reference statements)

Supporting

Mentioning

225

Contrasting

Order By: Relevance

“…However, supercooled liquids can also exhibit complicated natures, displaying anisotropic mechanical responses, anisotropic fluctuations [47], and negative shear modulus and negative stress correlations. An understanding of the mechanism underlying these complicated phenomena will lead us to a better comprehension of the violations of the FDT [1][2][3][4][5][6] that they involve, as well as certain consequent modifications of the concept of an effective temperature [13][14][15][16][17][18][19][20][21]. Supercooled liquids composed of spherical or low-molecularweight molecules may be excellent materials for investigating non-equilibrium statistical mechanics.…”

Section: Resultsmentioning

confidence: 99%

“…The relationship between the response and correlation functions is of great interest and importance [1][2][3][4][5][6][13][14][15][16][17][18][19][20][21]. If we use the shear moduli G …”

Section: Violation Of Fluctuation-dissipation Theoremmentioning

confidence: 99%

“…The FDT relates the response functions to the associated correlation functions and holds in equilibrium states but is typically violated for non-equilibrium states. Much work has been devoted to understanding the relationship between response functions and correlation functions in nonequilibrium situations; however, this relationship remains unclear [1][2][3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Mechanical responses and stress fluctuations of a supercooled liquid in a sheared non-equilibrium state

Mizuno

Yamamoto

2012

Eur. Phys. J. E

View full text Add to dashboard Cite

Abstract.A steady shear flow can drive supercooled liquids into a non-equilibrium state. Using molecular dynamics simulations under steady shear flow superimposed with oscillatory shear strain for a probe, non-equilibrium mechanical responses are studied for a model supercooled liquid composed of binary soft spheres. We found that even in the strongly sheared situation, the supercooled liquid exhibits surprisingly isotropic responses to oscillating shear strains applied in three different components of the strain tensor. Based on this isotropic feature, we successfully constructed a simple two-mode Maxwell model that can capture the key features of the storage and loss moduli, even for highly non-equilibrium state. Furthermore, we examined the correlation functions of the shear stress fluctuations, which also exhibit isotropic relaxation behaviors in the sheared non-equilibrium situation. In contrast to the isotropic features, the supercooled liquid additionally demonstrates anisotropies in both its responses and its correlations to the shear stress fluctuations. Using the constitutive equation (a two-mode Maxwell model), we demonstrated that the anisotropic responses are caused by the coupling between the oscillating strain and the driving shear flow. Due to these anisotropic responses and fluctuations, the violation of the fluctuation-dissipation theorem (FDT) is distinct for different components. We measured the magnitude of this violation in terms of the effective temperature. It was demonstrated that the effective temperature is notably different between different components, which indicates that a simple scalar mapping, such as the concept of an effective temperature, oversimplifies the true nature of supercooled liquids under shear flow. An understanding of the mechanism of isotropies and anisotropies in the responses and fluctuations will lead to a better appreciation of these violations of the FDT, as well as certain consequent modifications to the concept of an effective temperature.

show abstract

Section: Resultsmentioning

confidence: 99%

“…The relationship between the response and correlation functions is of great interest and importance [1][2][3][4][5][6][13][14][15][16][17][18][19][20][21]. If we use the shear moduli G …”

Section: Violation Of Fluctuation-dissipation Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Mechanical responses and stress fluctuations of a supercooled liquid in a sheared non-equilibrium state

Mizuno

Yamamoto

2012

Eur. Phys. J. E

View full text Add to dashboard Cite

show abstract

“…Our goal in the present work is to show how the cell body's random pull-andpush can be investigated by means of very recent theoretical advances in the field of non-equilibrium statistical mechanics. And indeed, from the theory standpoint, in the recent past, much effort has been invested in deriving simple generalizations or extensions of the celebrated fluctuation-dissipation theorem for systems that can be arbitrarily far out of equilibrium [5,[11][12][13][14][15][16][17][18][19][20][21][22][23]. These efforts have given birth to a flurry of formulas relating the response of a system to a small external perturbation to some correlation functions, even when the system is not in an equilibrium state.…”

mentioning

confidence: 99%

Probing active forces via a fluctuation-dissipation relation: Application to living cells

Bohec¹,

Gallet²,

Maes³

et al. 2013

EPL

View full text Add to dashboard Cite

PACS 05.40.a -Fluctuations phenomena, random processes, noise, and Brownian motion PACS 87.18.Tt -Noise in biological systems PACS 87.16.Nn -Motor proteins (myosin, kinesin dynein)Abstract. -We derive a new fluctuation-dissipation relation for non-equilibrium systems with long term memory. We show how this relation allows one to access new experimental information regarding active forces in living cells that cannot otherwise be accessed. For a silica bead attached to the wall of a living cell, we identify a cross-over time between thermally controlled fluctuations and those produced by the active forces. We show that the probe position is eventually slaved to the underlying random drive produced by the so-called active forces.Living cells are paradigmatic out of equilibrium systems, subjected to the ATP-driven activity of a collection of molecular motors, whose individual motion cannot easily be disentangled from thermal fluctuations. These are relatively small systems for which fluctuation phenomena are prominent, as investigated in recent works [1][2][3][4][5][6][7][8][9], with specific focus on the active forces and non-Newtonian rheology [1-3, 10] which can be measured via micro-rheological devices. Our goal in the present work is to show how the cell body's random pull-andpush can be investigated by means of very recent theoretical advances in the field of non-equilibrium statistical mechanics. And indeed, from the theory standpoint, in the recent past, much effort has been invested in deriving simple generalizations or extensions of the celebrated fluctuation-dissipation theorem for systems that can be arbitrarily far out of equilibrium [5,[11][12][13][14][15][16][17][18][19][20][21][22][23]. These efforts have given birth to a flurry of formulas relating the response of a system to a small external perturbation to some correlation functions, even when the system is not in an equilibrium state. Yet, so far none of these formulas has been of any predictive power in an actual experimental system. Existing experiments revolving around these theoretical advances have been confined to refined and nontrivial confirmations that in some small scale systems such as an optically trapped Brownian particle [24][25][26] the various ingredients entering these extended fluctuation-dissipation relations (EFDR) can indeed be measured. Given that the dynamics of (a) Correspondig Author: paolo.visco@univ-paris-diderot.fr living cells exhibit strong memory effects, we will first have to derive our own version of an EFDR adapted to a system with stochastic yet non-Markovian dynamics. The latter EFDR and its consequence for the understanding of active forces are the central topics of this letter. For instance, how relevant is the long term memory in relating response and fluctuations? What new pieces of information on non-equilibrium forces can be learnt from such a relationship? Can thermal fluctuations be disentangled from those arising from the active forces in a quantitative way? These are the questions we wish to address i...

show abstract

“…Following previous work on nonequilibrium linear response [3,4,1] we speak about an entropic and a frenetic contribution; see also Appendix A. The entropic part is purely dissipative and is proportional to the noise correlation; the frenetic component takes into account the changes in dynamical activity due to the perturbation.…”

Section: Second Fluctuation-dissipation Relationmentioning

confidence: 99%

Friction and noise for a probe in a nonequilibrium fluid

Maes

Steffenoni

2015

Phys. Rev. E

Self Cite

View full text Add to dashboard Cite

Abstract. We investigate the fluctuation dynamics of a probe around a deterministic motion induced by interactions with driven particles. The latter constitute the nonequilibrium medium in which the probe is immersed and is modelled as overdamped Langevin particle dynamics driven by nonconservative forces. The expansion that yields the friction and noise expressions for the reduced probe dynamics is based on linear response around a time-dependent nonequilibrium condition of the medium. The result contains an extension of the second fluctuation-dissipation relation between friction and noise for probe motion in a nonequilibrium fluid. The problemWhether the environment of a system is in equilibrium or is driven into a nonequilibrium condition is important for characterizing internal motions and reactions. In other words the reduced system dynamics will reflect whether the environment is driven or not.For example, the relation between noise and friction on the system need no longer be described via the standard second fluctuation-dissipation (or Einstein) relation, we cannot unambiguously speak about entropy fluxes into the environment in terms of heat as there would be no Clausius relation, and system fluctuations or noise level in general are not simply quantified by a reservoir temperature. The present paper takes up the challenge of characterizing such an effective dynamics for a probe in contact with a nonequilibrium medium. One should have in mind that the medium consists of active elements or driven particles themselves in contact with a big thermal equilibrium reservoir (like surrounding air or water). Combined, the medium and the heat bath make up the nonequilibrium fluid. The system is called a probe here, but it can in general also refer to a collective or with j = 1, . . . , N labeling the particles and subject to independent standard white noises ξ j t . The β denotes the inverse temperature of the background equilibrium reservoir but the particles are effectively driven by the nonconservative force F . For simplicity we have not introduced explicitly friction and mass parameters, keeping only λ (coupling) and β as parameters. The particle interaction is given through the potential Φ while the potential U depends on the position X t of the probe, thus representing the back-reaction of the probe on each particle. Other and different types of interaction between probe and medium are possible, e.g. in terms of their center of mass coordinate with a mean field type potential U ( j x j t − X t ), here not discussed and inessential for the present level of discussion. Keeping to (1.1) the probe dynamics itself iswhere we indicate by K X t ,Ẋ t other aspects of the probe motion in the fluid. Its mass M is obviously also an important parameter for separation of time-scales between probe and fluid particle motion.The equations (1.1) and (1.2) starting at t = 0 are the basic evolution equations representing the coupled dynamics of probe and fluid particles. Nonequilibrium works directly on the medium which is ...

show abstract

Nonequilibrium Linear Response for Markov Dynamics, I: Jump Processes and Overdamped Diffusions

Cited by 124 publications

References 48 publications

Mechanical responses and stress fluctuations of a supercooled liquid in a sheared non-equilibrium state

Mechanical responses and stress fluctuations of a supercooled liquid in a sheared non-equilibrium state

Probing active forces via a fluctuation-dissipation relation: Application to living cells

Friction and noise for a probe in a nonequilibrium fluid

Contact Info

Product

Resources

About