Harmonic Systems with Bulk Noises

Bernardin, Cédric; Kannan, Venkateshan; Lebowitz, Joel L.; Lukkarinen, Jani

doi:10.1007/s10955-011-0416-3

Cited by 28 publications

(50 citation statements)

References 24 publications

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“…As in [7], we could consider a more general model, with a pinning potential. Instead of the deformation r x , we now introduce the position q x of the particle x.…”

Section: Remarksmentioning

confidence: 99%

Hydrodynamic Limit for the Velocity-Flip Model

Simon

2014

Springer Proceedings in Mathematics &Amp; Statistics

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We study the diffusive scaling limit for a chain of N coupled oscillators. In order to provide the system with good ergodic properties, we perturb the Hamiltonian dynamics with random flips of velocities, so that the energy is locally conserved. We derive the hydrodynamic equations by estimating the relative entropy with respect to the local equilibrium state, modified by a correction term.Acknowledgements. I thank Cédric Bernardin and Stefano Olla for giving me this problem, and for the useful discussions and suggestions on this work.

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“…As in [7], we could consider a more general model, with a pinning potential. Instead of the deformation r x , we now introduce the position q x of the particle x.…”

Section: Remarksmentioning

confidence: 99%

Hydrodynamic Limit for the Velocity-Flip Model

Simon

2014

Springer Proceedings in Mathematics &Amp; Statistics

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“…1(b). Heat conduction and the entropy production in harmonic systems have long been studied [14,[20][21][22][23][24][25]. In contrast to the previous works, our study focuses on the role of the slow and fast variable.…”

Section: Introductionmentioning

confidence: 99%

Hidden entropy production by fast variables

Chun

Noh

2015

Phys. Rev. E

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We investigate nonequilibrium underdamped Langevin dynamics of Brownian particles that interact through a harmonic potential with coupling constant K and are in thermal contact with two heat baths at different temperatures. The system is characterized by a net heat flow and an entropy production in the steady state. We compare the entropy production of the harmonic system with that of Brownian particles linked with a rigid rod. The harmonic system may be expected to reduce to the rigid rod system in the infinite K limit. However, we find that the harmonic system in the K → ∞ limit produces more entropy than the rigid rod system. The harmonic system has the center of mass coordinate as a slow variable and the relative coordinate as a fast variable. By identifying the contributions of the degrees of freedom to the total entropy production, we show that the hidden entropy production by the fast variable is responsible for the extra entropy production. We discuss the K dependence of each contribution.

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“…This model is explicit enough to be studied rigorously, even in the thermodynamic limit: I quote below some of the results proven in [1] (without pinning) and in [4] (with pinning).…”

Section: Comparison Of Energy Fluctuations At the Nessmentioning

confidence: 99%

“…The fields R N t and Y N t can also be interpreted as time-dependent distributions. We argue in [1] that R N t → R t and Y N t → Y t , in the sense of distributions as N → ∞, and that the limit distributions solve the following stochastic differential equations:…”

Section: Fluctuating Hydrodynamics Of the Velocity Flip Modelmentioning

confidence: 99%

Energy fluctuations, hydrodynamics and local correlations in harmonic systems with bulk noises

Lukkarinen¹

2012

Phys. Scr.

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In this note, I summarise and comment on joint work with C. Bernardin, V. Kannan, and J. L. Lebowitz concerning two harmonic systems with bulk noises whose nonequilibrium steady states (NESS) are nearly identical (they share the same thermal conductivity and two-point function), but whose hydrodynamic properties (convergence towards the NESS) are very different. The goal is to discuss the results in the general context of nonequilibrium properties of dynamical systems, in particular, what they tell us about possible effective models, or predictive approximations, for such systems.

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Harmonic Systems with Bulk Noises

Cited by 28 publications

References 24 publications

Hydrodynamic Limit for the Velocity-Flip Model

Hydrodynamic Limit for the Velocity-Flip Model

Hidden entropy production by fast variables

Energy fluctuations, hydrodynamics and local correlations in harmonic systems with bulk noises

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