A Framework of Nonequilibrium Statistical Mechanics. II. Coarse-Graining

Montefusco, Alberto; Peletier, Mark A.; Öttinger, Hans Christian

doi:10.1515/jnet-2020-0069

Cited by 11 publications

(3 citation statements)

References 64 publications

(112 reference statements)

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“…In this respect, it is crucial to examine whether the fluctuations can be represented adequately in terms of stochastic differential equations (SDE) as discussed in Sect. 5, or whether there are rather rare but large events that prevail [88], where the latter would require other means of coarse graining (e.g., see [72,73]). An equally important question is the one of time-scale separation between the different levels of description; a lack of time-scale separation (as observed, e.g., in dislocation systems [89]) complicates the coarse graining significantly.…”

Section: Discussionmentioning

confidence: 99%

“…The evolution of the natural configuration can therefore be imagined as a jump process between local minima [70,71]. If these jumps are rare events, the coarse graining procedure needs to reflect that aspect properly [72,73]. In the following, it is assumed for the purpose of illustration that the dynamics of {R α } takes the form of a SDE with multiplicative noise, using the Itô interpretation of stochastic calculus [56,57],…”

Section: Derivation Of Friction Operator By Coarse Grainingmentioning

confidence: 99%

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Particle-based approach to the Eulerian distortion field and its dynamics

Hütter

Pavelka

2023

Continuum Mech. Thermodyn.

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The Eulerian distortion field is an essential ingredient for the continuum modeling of finite elastic and inelastic deformations of materials; however, its relation to finer levels of description has not yet been established. This paper provides a definition of the Eulerian distortion field in terms of the arrangement of the constituent microscopic particles, which is beneficial for fundamental studies as well as for the analysis of computer simulations, e.g., molecular dynamics simulations. Using coarse graining and nonequilibrium thermodynamics, the dynamics of the Eulerian distortion field is examined in detail and related to the underlying dynamics of the particles. First, the usual kinematics of the distortion and the known expression for the Cauchy stress tensor are recovered. And second, it is found that the Mandel stress and the plastic deformation-rate tensor in the natural configuration constitute the relevant force–flux pair for the relaxation of the distortion. Finally, the procedure is illustrated on two examples, namely on an amorphous solid and on a crystalline solid with one slip system.

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Section: Discussionmentioning

confidence: 99%

Section: Derivation Of Friction Operator By Coarse Grainingmentioning

confidence: 99%

Particle-based approach to the Eulerian distortion field and its dynamics

Hütter

Pavelka

2023

Continuum Mech. Thermodyn.

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“…To overcome numerical and theoretical difficulty, the most common approach neglects some "details" of the system (namely, the dynamics of the solvent molecules) in favor of a mesoscopic description in terms of random variables: This corresponds to a temporal and spatial coarse graining. Since one can introduce different possible mesoscopic descriptions, usually different levels of coarse graining are allowed [7]. Therefore, evaluating the consequences of the coarse graining on the physical properties of the system is a general issue of indisputable importance.…”

Section: Introductionmentioning

confidence: 99%

Excess and loss of entropy production for different levels of coarse graining

2021

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We investigate the effect of coarse graining on the thermodynamic properties of a system, focusing on entropy production. As a case of study, we consider a one-dimensional colloidal particle in contact with a thermal bath, moving in a sinusoidal potential and driven out of equilibrium by a small constant force. Different levels of coarse graining are evaluated: At first, we compare the results in the underdamped dynamics with those in the overdamped one (first coarse graining). For large values of the friction coefficient, the two dynamics have the same thermodynamics properties, while, for smaller friction values, the overdamped approximation produces an excess of entropy production with respect to that of the underdamped dynamics. Moreover, for further smaller values of the drag coefficient, the excess of entropy production turns into a loss. These regimes are explained by evaluating the jump statistics, observing that the inertia is able to induce multiple jumps and affect the average jump rate. The periodic shape of the potential allows us to approximate the continuous dynamics via a Markov chain after the introduction of a suitable time and space discretization (second level of coarse graining). This discretization procedure is implemented starting both from the underdamped and the overdamped evolution and is analyzed for different values of the friction coefficient.

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Discrete defect plasticity and implications for dissipation

Needleman

2023

European Journal of Mechanics - A/Solids

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A Framework of Nonequilibrium Statistical Mechanics. II. Coarse-Graining

Cited by 11 publications

References 64 publications

Particle-based approach to the Eulerian distortion field and its dynamics

Particle-based approach to the Eulerian distortion field and its dynamics

Excess and loss of entropy production for different levels of coarse graining

Discrete defect plasticity and implications for dissipation

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