Transition from kinetic theory to nonlocal hydrodynamics and the law of increasing entropy

Abstract

It has been shown previously that for weak hydrodynamic sources the kinetic description of a gas is equivalent to the hydrodynamic description in which the physical relations are nonlocal in space and time. This work investigates the form of the sources with a transition from kinetics to hydrodynamics together with the law of nonnegative entropy production for a nonrelativistic gas. It is shown that within the scope of perturbation theory this condition is satisfied by all systems for which the sources are hydrodynamic in the first approximation. A class of sources is also found to satisfy this condition beyond the scope of perturbation theory, i.e., in the highly nonlinear situation. A recursion scheme for calculation of the physical relations is derived for this case. The results of this work are independent of the explicit form of the collision integral.