Non-Markovian systems out of equilibrium: exact results for two routes of coarse graining

Jung, Gerhard

doi:10.1088/1361-648x/ac56a7

Cited by 9 publications

(23 citation statements)

References 65 publications

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“…In future work, it could be useful to attempt a similar derivation as in [29] using the Mori-Zwanzig projection operator method to derive the GLE but crucially including also the derivation of the memory kernel. This could be done, e.g., by taking advantage of very recent advances in the field of memory kernel-reconstruction techniques for systems out of equilibrium [37,60].…”

Section: Discussionmentioning

confidence: 99%

“…Shear-flow systems have been studied as examples of driven systems to investigate the validity of fluctuationdissipation relations out of equilibrium [23,31,32]. It was found that the first fluctuation-dissipation theorem (FDT) is different from the equilibrium case [32][33][34][35] but, on the other hand, according to some recent studies [36,37], the second FDT should be valid even far from equilibrium. For this reason, the second FDT allows one to study some properties of a system even in more general cases such as far from equilibrium.…”

Section: Introductionmentioning

confidence: 99%

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Generalized Langevin equation with shear flow and its fluctuation-dissipation theorems derived from a Caldeira-Leggett Hamiltonian

Sara¹,

Zaccone²

2023

Preprint

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We provide a first-principles derivation of the Langevin equation with shear flow and its corresponding fluctuation-dissipation theorems. Shear flow of simple fluids has been widely investigated by numerical simulations. Most studies postulate a Markovian Langevin equation with a simple shear drag term à la Stokes. However, this choice has never been justified from first principles. We start from a particle-bath system described by a classical Caldeira-Leggett Hamiltonian modified by adding a term proportional to the strain-rate tensor according to Hoover's DOLLS method, and we derive a generalized Langevin equation for the sheared system. We then compute, analytically, the noise time-correlation functions in different regimes. Based on the intensity of the shear-rate, we can distinguish between close-to-equilibrium and far-from-equilibrium states. According to the results presented here, the standard, simple and Markovian form of the Langevin equation with shear flow postulated in the literature is valid only in the limit of extremely weak shear rates compared to the effective vibrational temperature of the bath. For even marginally higher shear rates, the (generalized) Langevin equation is strongly non-Markovian and non-trivial fluctuation-dissipation theorems are derived.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generalized Langevin equation with shear flow and its fluctuation-dissipation theorems derived from a Caldeira-Leggett Hamiltonian

Sara¹,

Zaccone²

2023

Preprint

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“…In this section, we briefly review recent advances in both of these directions. More detailed perspectives for each approach can be found in refs ( 332 ) and ( 333 ) for molecular CG modeling at equilibrium and in ref ( 334 ) for out of equilibrium conditions. Furthermore, ref ( 335 ) provides a general review of CG modeling for both in and out of equilibrium conditions.…”

Section: Dynamics Of the Coarse-grained Modelsmentioning

confidence: 99%

Bottom-up Coarse-Graining: Principles and Perspectives

Jin

Pak

Durumeric

et al. 2022

J. Chem. Theory Comput.

148

147

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Large-scale computational molecular models provide scientists a means to investigate the effect of microscopic details on emergent mesoscopic behavior. Elucidating the relationship between variations on the molecular scale and macroscopic observable properties facilitates an understanding of the molecular interactions driving the properties of real world materials and complex systems (e.g., those found in biology, chemistry, and materials science). As a result, discovering an explicit, systematic connection between microscopic nature and emergent mesoscopic behavior is a fundamental goal for this type of investigation. The molecular forces critical to driving the behavior of complex heterogeneous systems are often unclear. More problematically, simulations of representative model systems are often prohibitively expensive from both spatial and temporal perspectives, impeding straightforward investigations over possible hypotheses characterizing molecular behavior. While the reduction in resolution of a study, such as moving from an atomistic simulation to that of the resolution of large coarse-grained (CG) groups of atoms, can partially ameliorate the cost of individual simulations, the relationship between the proposed microscopic details and this intermediate resolution is nontrivial and presents new obstacles to study. Small portions of these complex systems can be realistically simulated. Alone, these smaller simulations likely do not provide insight into collectively emergent behavior. However, by proposing that the driving forces in both smaller and larger systems (containing many related copies of the smaller system) have an explicit connection, systematic bottom-up CG techniques can be used to transfer CG hypotheses discovered using a smaller scale system to a larger system of primary interest. The proposed connection between different CG systems is prescribed by (i) the CG representation (mapping) and (ii) the functional form and parameters used to represent the CG energetics, which approximate potentials of mean force (PMFs). As a result, the design of CG methods that facilitate a variety of physically relevant representations, approximations, and force fields is critical to moving the frontier of systematic CG forward. Crucially, the proposed connection between the system used for parametrization and the system of interest is orthogonal to the optimization used to approximate the potential of mean force present in all systematic CG methods. The empirical efficacy of machine learning techniques on a variety of tasks provides strong motivation to consider these approaches for approximating the PMF and analyzing these approximations.

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“…Important conclusions from these studies are that the 2FDT is no longer generally valid in such cases: namely, in the presence of non-linear or stochastic interactions, 45,46 external forces, or general non-equilibrium settings. 47 Furthermore, additional terms in this relation can emerge. 35,36,45,48 In this work we will take a complementary approach and use the GLE (1) as a starting point to extract effective equations of motion for the coarse-grained variables from microscopic simulations.…”

Section: Introductionmentioning

confidence: 99%

“…What happens in active systems far from equilibrium? This question has been intensely discussed in the literature, 19,22,23,47,49,[53][54][55][56][57] often focusing on the question of whether the 2FDT is still fulfilled. However, as mentioned above, one has some freedom as to how to distribute the net bath forces between the different terms of the GLE.…”

Section: Introductionmentioning

confidence: 99%