Derivation in a nonequilibrium ensemble formalism of a far-reaching generalization of a quantum Boltzmann theory

Ramos, J. Galvão; Vasconcellos, Áurea R.; Luzzi, Roberto

doi:10.1016/s0378-4371(00)00173-4

Cited by 6 publications

(3 citation statements)

References 22 publications

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“…can be considered as a generalized Boltzmann single-particle distribution function, which in the framework of the NESEF-based kinetic theory 10,27,28 satisfies. 29,30 But, for our purposes here of building a generalized nonlinear thermo-hydrodynamics (that is, the thermal physics of continuous media), it is highly convenient to resort to an equivalent nonequilibrium mesoscopic-level in what can be referred-to as a grand-canonical ensemble. This is described elsewhere.…”

Section: Nonlinear Higher-order Hydrodynamics (Brief Description)mentioning

confidence: 99%

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Nonlinear higher-order hydrodynamics: Fluids under driven flow and shear pressure

et al. 2021

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In the context of a nonequilibrium statistical thermodynamics-based on a nonequilibrium statistical ensemble formalism-a generalized hydrodynamics of fluids under driven flow and shear stress is derived. At the thermodynamic level, the nonequilibrium equations of state are derived, which are coupled to the evolution of the basic variables that describe the hydrodynamic motion in such a system. Generalized diffusion-advection and Maxwell-Cattaneo advection equations are obtained in appropriate limiting situations. This nonlinear higher-order hydrodynamics is applied, in an illustration, to the case of a dilute solution of Brownian particles in nonequilibrium conditions and flowing in a solvent acting as a thermal bath. This is done in the framework of such generalized hydrodynamics but truncated up to a second order.

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Section: Nonlinear Higher-order Hydrodynamics (Brief Description)mentioning

confidence: 99%

“…( 26) define a space of nonequilibrium thermodynamic states that describes the macroscopic state of the system as does the set of basic variables of Eqs. ( 27)- (30). These equations relate both types of nonequilibrium thermodynamics variables and, thus, Eqs.…”

Section: Nonlinear Higher-order Hydrodynamics (Brief Description)mentioning

confidence: 99%

Nonlinear higher-order hydrodynamics: Fluids under driven flow and shear pressure

et al. 2021

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“…It also contains a large generalization of Boltzmann's transport theory, with the original Boltzmann equation for the one-particle distribution retrieved under stringent asymptotic limiting conditions; details and discussions are given in Refs. [33] and [62].…”

Section: A Nonequilibrium Statistical Ensemble Formalismmentioning

confidence: 99%

Thermo-statistics of irreversible processes: a Boltzmann-Gibbs-style ensemble formalism

Luzzi¹,

Vasconcellos²,

Ramos³

2006

Braz. J. Phys.

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The area of Physics indicated in the title is nowadays of quite relevant interest, not only from the purely scientific point of view, but specially for its applied aspects associated to the present-time point-first-technologies. A particular research trend in the theory of irreversible processes, which are evolving in time in systems arbitrarily departed from equilibrium, is here briefly described. It consists in the construction of a Gibbs-style nonequilibrium ensemble formalism. The derivation of a nonequilibrium statistical operator is described (the variational approach of Predictive Statistical Mechanics is used). The main questions involved are presented and applications are briefly mentioned.

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Generalized Kinetic Equation for Far-from-Equilibrium Many-Body Systems

et al. 2011

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Derivation in a nonequilibrium ensemble formalism of a far-reaching generalization of a quantum Boltzmann theory

Cited by 6 publications

References 22 publications

Nonlinear higher-order hydrodynamics: Fluids under driven flow and shear pressure

Nonlinear higher-order hydrodynamics: Fluids under driven flow and shear pressure

Thermo-statistics of irreversible processes: a Boltzmann-Gibbs-style ensemble formalism

Generalized Kinetic Equation for Far-from-Equilibrium Many-Body Systems

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