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Claus, Isabelle; Gaspard, Pierre

doi:10.1023/a:1026447129361

Cited by 18 publications

(17 citation statements)

References 23 publications

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“…This analysis and the knowledge of these coefficients allow us to obtain the macroscopic reaction-diffusion equations. These equations present cross-diffusion terms which are induced by the reaction if the reaction probability p 0 is not vanishing, as in the previous studies of the reactive periodic Lorentz gas and multibaker models [20,21,24,25,26]. In the reactive random Lorentz gas, our analysis shows that a transition happens in the reaction sector between a regime at low concentrations of catalytic disks and reaction probabilities and another one at high concentrations and probabilities.…”

Section: Interpretation Of the Gradient Terms In The Entropysupporting

confidence: 64%

“…The catalytic disks are few among the disks which compose the Lorentz gas. Spatially periodic Lorentz gas and multibaker models with reaction A ⇋ B have been studied in detail and their diffusive and reactive modes were constructed together with their dispersion relations [24,25,26]. In this way, the macroscopic reaction-diffusion equations could be derived in a systematic way from the underlying dynamics.…”

Section: Introductionmentioning

confidence: 99%

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Entropy production in diffusion-reaction systems: The reactive random Lorentz gas

Mátyás

Gaspard

2005

Phys. Rev. E

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We report the study of a random Lorentz gas with a reaction of isomerization A<==>B between two colors of moving particles elastically bouncing on hard disks. The reaction occurs when the moving particles collide on catalytic disks, which constitute a fraction of all the disks. Under dilute-gas conditions, the reaction-diffusion process is ruled by two coupled Boltzmann-Lorentz equations for the distribution functions of the colors. The macroscopic reaction-diffusion equations with cross-diffusion terms induced by the chemical reaction are derived from the kinetic equations. We use an H theorem of the kinetic theory in order to derive a macroscopic entropy depending on the gradients of color densities and which has a non-negative entropy production in agreement with the second law of thermodynamics.

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Section: Interpretation Of the Gradient Terms In The Entropysupporting

confidence: 64%

Section: Introductionmentioning

confidence: 99%

Entropy production in diffusion-reaction systems: The reactive random Lorentz gas

Mátyás

Gaspard

2005

Phys. Rev. E

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“…(65) as shown elsewhere [23]. Beside the diffusive modes, the chemical modes can also be constructed in models of reaction-diffusion processes [33][34][35][36].…”

Section: Periodic Yukawa-potential Lorentz Gasmentioning

confidence: 99%

Time Asymmetry in Nonequilibrium Statistical Mechanics

Gaspard

2007

Advances in Chemical Physics

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An overview is given on the recent understanding of time asymmetry in nonequilibrium statistical mechanics. This time asymmetry finds its origin in the spontaneous breaking of the time-reversal symmetry at the statistical level of description. The relaxation toward the equilibrium state can be described in terms of eigenmodes of fundamental Liouville's equation of statistical mechanics. These eigenmodes are associated with Pollicott-Ruelle resonances and correspond to exponential damping. These eigenmodes can be explicitly constructed in dynamical systems sustaining deterministic diffusion, which shows their singular character. The entropy production expected from nonequilibrium thermodynamics can be derived ab initio thanks to this construction. In the escape-rate theory, the transport coefficients can be related to the leading Pollicott-Ruelle resonance of open systems and to the characteristic quantities of the microscopic dynamics. In nonequilibrium steady states, the entropy production is shown to result from a time asymmetry in the dynamical randomness of the nonequilibrium fluctuations. Furthermore, the generalizations of Onsager reciprocity relations to nonlinear response can be deduced from the fluctuation theorem for the currents. Furthermore, the principle of temporal ordering in nonequilibrium steady states is formulated and its perspectives for the generation of biological information are discussed.

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“…This is consistent with the fact that the reaction rate is largely independent of the local reaction rate at the catalysts in the diffusion-controled regime, as already noticed in Refs. [9,26]. Let us consider more explicitly the simple case L = 1.…”

Section: B Relaxation Rates and Eigenmodes Of The Reactive Operatormentioning

confidence: 99%

The fractality of the relaxation modes in reaction–diffusion systems

Claus¹,

Gaspard²

2002

Physica D: Nonlinear Phenomena

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In chaotic reaction-diffusion systems with two degrees of freedom, the modes governing the exponential relaxation to the thermodynamic equilibrium present a fractal structure which can be characterized by a Hausdorff dimension. For long wavelength modes, this dimension is related to the Lyapunov exponent and to a reactive diffusion coefficient. This relationship is tested numerically on a reactive multibaker model and on a two-dimensional periodic reactive Lorentz gas. The agreement with the theory is excellent.

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Untitled

Cited by 18 publications

References 23 publications

Entropy production in diffusion-reaction systems: The reactive random Lorentz gas

Entropy production in diffusion-reaction systems: The reactive random Lorentz gas

Time Asymmetry in Nonequilibrium Statistical Mechanics

The fractality of the relaxation modes in reaction–diffusion systems

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