Comments on the validity of the non-stationary generalized Langevin equation as a coarse-grained evolution equation for microscopic stochastic dynamics

Glatzel, Fabian; Schilling, Tanja

doi:10.1063/5.0049693

Cited by 8 publications

(6 citation statements)

References 20 publications

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“…A related question comprises the entropy production in such CG systems and whether it is possible to connect thermodynamic quantities such as entropy [37,38,54] as discussed intensively in the framework of stochastic thermodynamics [55][56][57] to dynamic coarsegraining, for example via projection operator techniques? We believe that answering these questions would pave the way towards systematic dynamic coarse-graining of nonequilibrium soft matter systems with applications to active microrheology [25,58], active matter [27,55,59], but also non-stationary situations such as crystallization [60], colloid self-assembly [61] or at phase transitions [62] using a nonstationary GLE [21,63].…”

Section: Discussionmentioning

confidence: 99%

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

Jung

2022

J. Phys.: Condens. Matter

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Generalized Langevin equations (GLEs) can be systematically derived via dimensional reduction from high-dimensional microscopic systems. For linear models the derivation can either be based on projection operator techniques such as the Mori-Zwanzig (MZ) formalism or by “integrating out” the bath degrees of freedom. Based on exact analytical results we show that both routes can lead to fundamentally diﬀerent GLEs and that the origin of these diﬀerences is based inherently on the non-equilibrium nature of the microscopic stochastic model. The most important conceptional diﬀerence between the two routes is that the MZ result intrinsically fulﬁlls the generalized second ﬂuctuation-dissipation theorem while the integration result can lead to its violation. We supplement our theoretical ﬁndings with numerical and simulation results for two popular non-equilibrium systems: Time-delayed feedback control and the active Ornstein-Uhlenbeck process.

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Section: Discussionmentioning

confidence: 99%

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

Jung

2022

J. Phys.: Condens. Matter

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“…A related question comprises the entropy production in such coarse-grained systems and whether it is possible to connect thermodynamic quantities such as entropy [37,38,50] as discussed intensively in the framework of stochastic thermodynamics [51][52][53] to dynamic coarse-graining, for example via projection operator techniques? We believe that answering these questions would pave the way towards systematic dynamic coarse-graining of non-equilibrium soft matter systems with applications to active microrheology [25,54], active matter [27,51,55], but also non-stationary situations such as crystallization [56], colloid self-assembly [57] or at phase transitions [58] using a non-stationary GLE [22,59].…”

Section: Discussionmentioning

confidence: 99%

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

Jung

2021

Preprint

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Generalized Langevin equations (GLEs) can be systematically derived via dimensional reduction from high-dimensional microscopic systems. For linear models the derivation can either be based on projection operator techniques such as the Mori-Zwanzig (MZ) formalism or by "integrating out" the bath degrees of freedom. Based on exact analytical results we show that both routes can lead to fundamentally different GLEs and that the origin of these differences is based inherently on the non-equilibrium nature of the microscopic stochastic model. The most important conceptional difference between the two routes is that the MZ result intrinsically fulfills the generalized second fluctuation-dissipation theorem while the integration result can lead to its violation. We supplement our theoretical findings with numerical and simulation results for two popular non-equilibrium systems: Time-delayed feedback control and the active Ornstein-Uhlenbeck process.

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“…A stochastic theory related to stochastic DDFT was derived using the Mori-Zwanzig formalism in [140]. Since the Mori-Zwanzig formalism continues to be improved [141][142][143][144], it is likely to play an important role also in future work on DDFT.…”

Section: Theoretical Developmentsmentioning

confidence: 99%

Perspective: New directions in dynamical density functional theory

Vrugt

Wittkowski

2022

J. Phys.: Condens. Matter

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Classical dynamical density functional theory (DDFT) has become one of the central modeling approaches in nonequilibrium soft matter physics. Recent years have seen the emergence of novel and interesting fields of application for DDFT. In particular, there has been a remarkable growth in the amount of work related to chemistry. Moreover, DDFT has stimulated research on other theories such as phase field crystal models and power functional theory. In this perspective, we summarize the latest developments in the field of DDFT and discuss a variety of possible directions for future research.

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Comments on the validity of the non-stationary generalized Langevin equation as a coarse-grained evolution equation for microscopic stochastic dynamics

Abstract: We recently showed that the dynamics of coarse-grained observables in systems out of thermal equilibrium are governed by the non-stationary generalized Langevin equation [

Cited by 8 publications

References 20 publications

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

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

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

Perspective: New directions in dynamical density functional theory

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