[en] The covariant entropy law is derived for an arbitrary choice of the hydrodynamic velocity field. The effects of the choices of Eckart and of Landau and Lifshits are shown. (Auth.)

[en] Published in summary form only

[en] H-theorems for two standard dynamics are proved by using a generalized Kullback-Leibler divergence which was recently introduced by the author [T. Yamano, J. Math. Phys. 50 (2009) 043302].

[en] A general method of constructing dissipative equations is developed, following Ehrenfest's idea of coarse graining. The approach resolves the major issue of discrete time coarse graining versus continuous time macroscopic equations. Proof of the H theorem for macroscopic equations is given, several examples supporting the construction are presented, and generalizations are suggested

[en] A relaxation-rate formula is presented for the entropic lattice Boltzmann model (ELBM) — a discrete kinetic theory for hydrodynamics. The simple formula not only guarantees the discrete time H-theorem but also gives full consideration to the consistency with hydrodynamics. The relaxation rate calculated with the formula effectively characterizes the drastic changes of the flow fields. By using this formula, the computational cost of the ELBM is significantly reduced and the model now can be efficiently used for a broad range of applications including high Reynolds number flows. (paper)

[en] The microscopic mechanics discovered by Nose, of which Gauss's isokinetic mechanics is a special case, makes it possible to simulate macroscopic irreversible nonequilibrium flows with purely reversible equations of motion. The Gauss-Nose and Nose-Hoover equations of motion explicitly include time-reversible momentum and energy reservoirs. Computer simulations of nonequilibrium steady-state systems described by Gauss-Nose mechanics invariably evolve in such a way as to increase entropy. The corresponding phase-space distribution functions, which include reservoir degrees of freedom, collapse onto stable strange attractors. Hypothetical time-reversed motions, which would violate the second law of thermodynamics, cannot be observed for two reasons: First, such reversed motions would occupy zero volume in the phase space; second, they would be dynamically unstable. Thus, Nose's reversible mechanics is fully consistent with irreversible thermodynamics, in the way forecast by Prigogine. That is, the consistency follows from the formulation of new microscopic equations of motion

[en] We consider entropy and relative entropy in field theory and establish relevant monotonicity properties with respect to the couplings. The relative entropy in a field theory with a hierarchy of renormalization-group fixed points ranks the fixed points, the lowest relative entropy being assigned to the highest multicritical point. We argue that as a consequence of a generalized H theorem Wilsonian RG flows induce an increase in entropy and propose the relative entropy as the natural quantity which increases from one fixed point to another in more than two dimensions. copyright 1996 The American Physical Society

[en] Extensive tables of the values of H-functions H⁰(z,ω) appropriate for the problems of radiative transfer in multiplying media characterized by ω >11, have been constructed correctly to the sixth decimal place for values of ω in the range 1.05-10. This accuracy has been attained with the aid of a 32-point Gaussian quadrature. (orig.)

[en] We describe a simple dynamical model of a one-dimensional ideal gas and use computer simulations of the model to illustrate two fundamental results of kinetic theory: the Boltzmann transport equation and the Boltzmann H-theorem. Although the model is time-reversal invariant, both results predict that the behaviour of the gas is time-asymmetric. We show that the assumption of molecular chaos is a necessary condition, but not a sufficient condition, for such time-asymmetric results to correctly describe the model, and we use computer simulations to investigate the conditions under which the assumption of molecular chaos holds.

[en] In this paper the generalizations of equations of chemical kinetics, including classical and quantum chemical kinetics, is considered. We make time discrete in these equations and prove the H-theorem. (paper)