Thermodynamic pressure in nonequilibrium gases

Domı́nguez, Raquel; Jou, David

doi:10.1103/physreve.51.158

Cited by 48 publications

(66 citation statements)

References 14 publications

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“…Such an exceptional condition means that the mass balance is determined by the transportation of the gases in the small hole. Therefore, the relevance of predictions by macroscopic theory 10,12 for the generalized Knudsen effect in which an equilibrium cell is connected with a nonequilibrium cell by a small hole is questionable.…”

Section: 12mentioning

confidence: 99%

“…7 On the other hand, some macroscopic phenomenologies for nonequilibrium steady states have been proposed. These are the Extended Thermodynamics (ET), 8 the Extended Irreversible Thermodynamics (EIT) [9][10][11] which is the combination of ET and information theory, and the Steady State Thermodynamics (SST). 12 It is interesting that both EIT and SST treat a common process in which a nonequilibrium cell is connected with an equilibrium cell.…”

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Knudsen Effect in a Nonequilibrium Gas

Nishino

Hayakawa

2005

J. Phys. Soc. Jpn.

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From the molecular dynamics simulation of a system of hard-core disks in which an equilibrium cell is connected with a nonequilibrium cell, it is confirmed that the pressure difference between two cells depends on the direction of the heat flux. From the boundary layer analysis, the velocity distribution function in the boundary layer is obtained. The agreement between the theoretical result and the numerical result is fairly good.

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Section: 12mentioning

confidence: 99%

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confidence: 99%

Knudsen Effect in a Nonequilibrium Gas

Nishino

Hayakawa

2005

J. Phys. Soc. Jpn.

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“…Finally, we briefly comment about EIT: Extended irreversible thermodynamics [19,20,21]. For an ideal gas, Refs.…”

Section: Discussionmentioning

confidence: 99%

Extended hydrodynamics from Enskog's equation: The bidimensional case

Ugawa

2005

Physica A: Statistical Mechanics and its Applications

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“…We cannot predict from the phenomenological equations that a molecular dynamics simulation of steady heat flow at large |Vr| will produce a non-analytic dependence on temperature gradient. This conclusion agrees with an analysis [8] where the scalar ae was the fraction of molecules excited in an internal vibration level.The more recent statistical developments [4,6] in extended thermodynamics have shown that when the system is a small volume V, the state variables are averages of microscopic operators taken over V. If we average Vp(R) over the points R in the interior of V, we obtain p(R+) -p(R-) where R± are points on opposite boundaries of the system, p(R+) is the density in the region on one side of Vand p(R_) the density on the other side. These variables characterize the state of the surroundings, not the internal state of V 9 described by ñ = Nm/V.…”

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Informational Extended Thermodynamics of Phonon and Self-Diffusion Components of Heat Conduction in Liquids

Nettleton¹

1998

Journal of Non-Equilibrium Thermodynamics

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Heat flow in a liquid is divided into a component carried by longitudinal sound and a component carried by self-diffusing molecules. These components are averages of operators for which expressions are given involving phonon numbers and the probability that a given molecule is free to diffuse out of its cage. On the informationtheoretic model, these operators can be used to calculate extended thermodynamic forces which are Lagrange multipliers used in maximizing the entropy. Following arguments that the two heat flux components are uncorrelated, we find forces and rate equations to be uncoupled in leading order. Analytic expressions for the forces can be used to calculate the non-linear dependence on the temperature gradient of the evolution equations for the heat flux components. Also, it is found that in a steady state the condition of constancy of the structural parameters does not lead to nonanalytic solutions far from equilibrium, and so pressure and viscosity will not depend non-analytically on the gradient of temperature. IntroductionFollowing a model of Debye [1] applied to gases, an early formulation of extended thermodynamics of heat conduction [2] in liquids adopted a phonon picture of transport. In this model, heat is carried by collective longitudinal hydrodynamic modes with wavelengths long in comparison with intermolecular spacing. In addition to the phonon mechanism, we can imagine a self-diffusion component. An atom, confined to a cage formed by neighbours, can occasionally diffuse away when a random superposition of high-frequency hypersound waves, with wavelengths of the order of intermolecular distances, causes a local expansion sufficient for escape from the cage. The diffusing molecule carries heat, producing heat flux J s which is added to the phonon component, Jp, to give the total heat flow, J.In accord with this picture, an extended thermodynamic treatment was proposed [3] based on coupled equations for J s and J p . It was also assumed that the time-rate of Brought to you by | Purdue University Libraries Authenticated Download Date | 6/13/15 2:29 AM 240 R· E. Nettleton change of the density gradient can be expressed in terms of J s and J p . This phenomenology evolved long before the informational approach [4, 5] to thermodynamics of heat conduction which allows us to calculate the entropy as a function of J s and J^, provided we have microscopic operators, J s and J p^ of which the fluxes are ensemble averages. By introducing an explicit function for J s , we can study the coupling of the heat flux components in the thermodynamic forces. The operators can also be used in a statistical derivation of the kinetic equations [6] to show that, in linear approximation, J s and J p obey independent Cattaneo-Vernottetype equations. This simplifies the earlier phenomenology [3], eliminating some of the coupling coefficients.The model for J 5 involves the probability Ë that an atom at r/ can cross the local potential barriers and move into a new cage. The relaxation of J s is coupled nonlinearly ...

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Thermodynamic pressure in nonequilibrium gases

Cited by 48 publications

References 14 publications

Knudsen Effect in a Nonequilibrium Gas

Knudsen Effect in a Nonequilibrium Gas

Extended hydrodynamics from Enskog's equation: The bidimensional case

Informational Extended Thermodynamics of Phonon and Self-Diffusion Components of Heat Conduction in Liquids

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