Existence of Nonequilibrium Steady State for a Simple Model of Heat Conduction

Li, Yao; Young, Lai Sang

doi:10.1007/s10955-013-0801-1

Cited by 10 publications

(13 citation statements)

References 31 publications

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“…For any probability measure µ on R N + , lim δ→0 µP δ − µ T V = 0.Proof. This proof is identical to that of Lemma 5.6 of[37].…”

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confidence: 54%

From billiards to thermodynamic laws: Stochastic energy exchange model

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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This paper studies a billiards-like microscopic heat conduction model, which describes the dynamics of gas molecules in a long tube with thermalized boundary. We numerically investigate the law of energy exchange between adjacent cells. A stochastic energy exchange model that preserves these properties is then derived. We further numerically justified that the stochastic energy exchange model preserves the ergodicity and the thermal conductivity of the original billiard model.

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“…For any probability measure µ on R N + , lim δ→0 µP δ − µ T V = 0.Proof. This proof is identical to that of Lemma 5.6 of[37].…”

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confidence: 54%

From billiards to thermodynamic laws: Stochastic energy exchange model

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…A second group consists of results for Hamiltonian models similar to those in [4], with additional assumptions or special features to make the problem more tractable (as noted earlier, Hamiltonian models are much harder), they include: [2,20], which prove ergodicity of the invariant measure assuming existence; [9], which proves existence and uniqueness for a model in which all energy exchanges are exclusively with 'thermostats' (or heat baths); and, [21], which treats a model with special geometry. A third group of results we know of consists of [10] and variants of this model [11,15]. As with the present study, models in this third group are stochastic versions of models with mechanical origin.…”

Section: Introductionmentioning

confidence: 63%

Nonequilibrium steady states for a class of particle systems

Young²

2014

Nonlinearity

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This paper contains rigorous results on nonequilibrium steady states for a class of particle systems coupled to unequal heat baths. These stochastic models are derived from the mechanical chains studied by Eckmann and Young by randomizing certain quantities while retaining other features of the model. Our results include the existence and uniqueness of nonequilibrium steady states, their relation to Lebesgue measure, tail bounds on total energy and number of particles in the system, and exponential convergence to steady states from suitable initial conditions.

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“…But many non-rigorous results are available. For example, many recent studies [21,16,30] consider the Markov energy exchange models obtained from nonrigorous derivations in [14,13,15]. Also see [19] for a review of many numerical and analytical results.…”

Section: Introductionmentioning

confidence: 99%

From deterministic dynamics to thermodynamic laws II: Fourier's law and mesoscopic limit equation

2019

Preprint

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This paper consider the mesoscopic limit of a stochastic energy exchange model that is numerically derived from deterministic dynamics. The law of large numbers and the central limit theorems are proved. We show that the limit of the stochastic energy exchange model is a discrete heat equation that satisfies Fourier's law. In addition, when the system size (number of particles) is large, the stochastic energy exchange is approximated by a stochastic differential equation, called the mesoscopic limit equation.

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Existence of Nonequilibrium Steady State for a Simple Model of Heat Conduction

Cited by 10 publications

References 31 publications

From billiards to thermodynamic laws: Stochastic energy exchange model

From billiards to thermodynamic laws: Stochastic energy exchange model

Nonequilibrium steady states for a class of particle systems

From deterministic dynamics to thermodynamic laws II: Fourier's law and mesoscopic limit equation

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