Apparent Violation of the Fluctuation-Dissipation Theorem due to Dynamic Heterogeneity in a Model Glass-Forming Liquid

Kawasaki, Takeshi; Tanaka, Hajime

doi:10.1103/physrevlett.102.185701

Cited by 17 publications

(14 citation statements)

References 35 publications

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“…These findings are correlated with recent numerical studies. 19,28,[56][57][58][59]95 Such strong deviations and decouplings between τ hetero and τ α when approaching the glass transition temperature have been observed in some experiments, 96,97 in which the lifetime of a subensemble is measured after selective excitation. Recent single-molecule experiments that detect the local mobility of probe molecules dispersed in glassy materials have other relevance to our simulations [98][99][100][101] .…”

Section: Conclusion and Final Remarksmentioning

confidence: 82%

“…20,23,55 On the contrary, other simulations show that the lifetime becomes much slower than the τ α as temperature decreases, and indicate that there exist deviations between the two time scales in glass-forming models. 19,28,[56][57][58][59] The aim of the present paper is to investigate the DH by numerically calculating the multi-time density correlation function, which is an elaboration of our previous study. 60 In this paper, we emphasize the essential consideration of the multi-time extension of the four-point correlation function that can aid in the elucidation of the time evolution of the correlated particle motions in the DH.…”

Section: Introductionmentioning

confidence: 99%

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Multi-time density correlation functions in glass-forming liquids: Probing dynamical heterogeneity and its lifetime

Kim

Saito

2010

The Journal of Chemical Physics

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A multi-time extension of a density correlation function is introduced to reveal temporal information about dynamical heterogeneity in glass-forming liquids. We utilize a multi-time correlation function that is analogous to the higher-order response function analyzed in multidimensional nonlinear spectroscopy. Here, we provide comprehensive numerical results of the four-point, three-time density correlation function from longtime trajectories generated by molecular dynamics simulations of glass-forming binary soft-sphere mixtures. We confirm that the two-dimensional representations in both time and frequency domains are sensitive to the dynamical heterogeneity and that these reveal the couplings of correlated motions, which exist over a wide range of time scales. The correlated motions detected by the three-time correlation function are divided into mobile and immobile contributions that are determined from the particle displacement during the first time interval. We show that the peak positions of the correlations are in accord with the information on the non-Gaussian parameters of the van Hove self-correlation function. Furthermore, it is demonstrated that the progressive changes in the second time interval in the three-time correlation function enable us to analyze how correlations in dynamics evolve in time. From this analysis, we evaluated the lifetime of the dynamical heterogeneity and its temperature dependence systematically. Our results show that the lifetime of the dynamical heterogeneity becomes much slower than the alpha-relaxation time that is determined from the two-point density correlation function when the system is highly supercooled.

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Section: Conclusion and Final Remarksmentioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Multi-time density correlation functions in glass-forming liquids: Probing dynamical heterogeneity and its lifetime

Kim

Saito

2010

The Journal of Chemical Physics

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“…In this case, the critical-like behaviour was observed for a dynamic quantity. We recently found that some glass-forming liquids exhibit critical-like behaviour of a 'static' structural quantity [7][8][9][10][11][12][13]. For example, our 3D hard-sphere-like (WCA) system exhibits Ising-like criticality of a hcp-like bond orientational order parameter, including the diverging correlation length ξ Q ∼ t −ν , where t = (T − T 0 )/T 0 (or t = (φ 0 − φ)/φ) and the diverging susceptibility χ Q ∼ t −γ , where ν = 0.63 and γ = 1.22 for 3D [12].…”

Section: Critical-like Behaviourmentioning

confidence: 99%

“…Its further extension to incorporate cooperative activated dynamics has also been made [6]. Contrary to the above-mentioned common belief that there is little structural change in a supercooled liquid, we have recently revealed that some model glass-forming systems exhibit temporal medium-range bond orientational order, whose correlation length appears to diverge towards the ideal glass transition temperature T 0 [7][8][9][10][11][12][13]. We emphasize that such bond orientational order is not easy to detect by the two-point density correlator, which may be a reason why this structural signature has not been recognized so far.…”

Section: Introductionmentioning

confidence: 99%

Roles of bond orientational ordering in glass transition and crystallization

Tanaka¹

2011

J. Phys.: Condens. Matter

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It is widely believed that crystallization in three dimensions is primarily controlled by positional ordering, and not by bond orientational ordering. In other words, bond orientational ordering is usually considered to be merely a consequence of positional ordering and thus has often been ignored. This one-order-parameter (density) description may be reasonable when we consider an equilibrium liquid-solid transition, but may not be enough to describe a metastable state and the kinetics of the transition. Here we propose that bond orientational ordering can play a key role in (i) crystallization, (ii) the ordering to quasi-crystal and (iii) vitrification, which occurs under rather weak frustration against crystallization. In a metastable supercooled state before crystallization, a system generally tends to have bond orientational order at least locally as a result of a constraint of dense packing. For a system interacting with hard-core repulsions, the constraint is intrinsically of geometrical origin and thus the basic physics is the same as nematic ordering of rod-like particles upon densification. Furthermore, positional ordering is easily destroyed even by weak frustration such as polydispersity and anisotropic interactions which favour a symmetry not consistent with that of the equilibrium crystal. Thus we may say that vitrification can be achieved by disturbing and prohibiting long-range positional ordering. Even in such a situation, bond orientational ordering still survives, accompanying its critical-like fluctuations, which are the origin of dynamic heterogeneity for this case. This scenario naturally explains both the absence of positional order and the development of bond orientational order upon cooling in a supercooled state. Although our argument is speculative in nature, we emphasize that this physical picture can coherently explain crystallization, vitrification, quasi-crystallization and their relationship in a natural manner. For a strongly frustrated system, even bond orientational order can be destroyed. Even in such a case there may still appear a structural signature of dense packing, which is linked to slow dynamics.

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“…For equilibrium systems, the FDTs can be rigorously derived within linear response theory [3,13], their validity in non-equilibrium situations has, however, been extensively and controversially discussed in the literature [9][10][11][14][15][16][17][18][19][20][21][22][23][24]. Outside the linear response regime, these theorems should therefore be rather seen as unproven "relations" [25].…”

Section: Introductionmentioning

confidence: 99%

Fluctuation-Dissipation Relations Far from Equilibrium: A Case Study

Jung¹,

Schmid²

2021

Preprint

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Fluctuation-dissipation relations or "theorems" (FDTs) are fundamental for statistical physics and can be rigorously derived for equilibrium systems. Their applicability to non-equilibrium systems is, however, debated. Here, we simulate an active microrheology experiment, in which a spherical colloid is pulled with a constant external force through a fluid, creating near-equilibrium and far-fromequilibrium systems. We characterize the structural and dynamical properties of these systems, and reconstruct an effective generalized Langevin equation (GLE) for the colloid dynamics. Specifically, we test the validity of two FDTs: The first FDT relates the non-equilibrium response of a system to equilibrium correlation functions, and the second FDT relates the memory friction kernel in the GLE to the stochastic force. We find that the validity of the first FDT depends strongly on the strength of the external driving: it is fulfilled close to equilibrium and breaks down far from it. In contrast, we observe that the second FDT is always fulfilled. We provide a mathematical argument why this generally holds for memory kernels reconstructed from a deterministic Volterra equation for correlation functions, even for non-stationary non-equilibrium systems.Motivated by the Mori-Zwanzig formalism, we therefore suggest to impose an orthogonality constraint on the stochastic force, which is in fact equivalent to the validity of this Volterra equation. Such GLEs automatically satisfy the second FDT and are unique, which is desirable when using GLEs for coarse-grained modeling.

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Apparent Violation of the Fluctuation-Dissipation Theorem due to Dynamic Heterogeneity in a Model Glass-Forming Liquid

Cited by 17 publications

References 35 publications

Multi-time density correlation functions in glass-forming liquids: Probing dynamical heterogeneity and its lifetime

Multi-time density correlation functions in glass-forming liquids: Probing dynamical heterogeneity and its lifetime

Roles of bond orientational ordering in glass transition and crystallization

Fluctuation-Dissipation Relations Far from Equilibrium: A Case Study

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