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A new kinetic model for binary mixtures and its Lattice Boltzman (LB) discretiza-tion is presented. In the hydrodynamic limit the model recovers the Navier-Stokes and the Stefan-Maxwell binary diffusion equations. The thermodynamic consistency is ensured by the defined non-negative entropy production within the domain of applicability of the model. The… (More)

We derive a one-parametric family of entropy functions that respect the additivity condition, and which describe effects of finiteness of statistical systems, in particular, distribution functions with long tails. This one-parametric family is different from the Tsallis entropies, and is a convex combination of the Boltzmann-Gibbs-Shannon entropy and the… (More)

In this paper, explicit method of constructing approximations (the triangle entropy method) is developed for nonequilibrium problems. This method enables one to treat any complicated nonlinear functionals that fit best the physics of a problem (such as, for example, rates of processes) as new independent variables. The work of the method is demonstrated on… (More)

Derivation of the lattice Boltzmann method from the continuous kinetic theory [X. He and L. S. Luo, Phys. Rev. E 55, R6333 (1997); X. Shan and X. He, Phys. Rev. Lett. 80, 65 (1998)] is extended in order to obtain boundary conditions for the method. For the model of a diffusively reflecting moving solid wall, the boundary condition for the discrete set of… (More)

The recently derived fluctuation-dissipation formula [A. N. Gorban et al., Phys. Rev. E 63, 066124 (2001)] is illustrated by the explicit computation for McKean's kinetic model [H. P. McKean, J. Math. Phys. 8, 547 (1967)]. It is demonstrated that the result is identical, on the one hand, to the sum of the Chapman-Enskog expansion, and, on the other hand, to… (More)

A theory of lattice Boltzmann (LB) models for hydrodynamic simulation is developed upon a novel relation between entropy construction and roots of Hermite polynomials. A systematic procedure is described for constructing numerically stable and complete Galilean invariant LB models. The stability of the new LB models is illustrated with a shock tube… (More)

A general geometrical framework of nonequilibrium thermodynamics is developed. The notion of macroscopically deenable ensembles is developed. The thesis about macroscopically deenable ensembles is suggested. This thesis should play the same role in the nonequilibrium thermodynamics, as the Church-Turing thesis in the theory of computability. The primitive… (More)