Suchergebnisse

Synopsis. — A generalization of the Boltzmann equation for a spatially inhomogeneous system is derived, resulting from a systematic linear approximation in the gradients following a method developed by Prigogine and coworkers. As a result an explicit expression of the inhomogeneous collision operator is given, in terms of the homogeneous operator only. Finally an application to the case of a hard sphere gas is discussed. For this special case, the annulation of a class of contributions is demonstrated, and the Enskog equation is obtained.

Synopsis. — The Bogolubov boundary conditions for the weakening of initial state correlations are used to write explicitely the equation in an inhomogeneous system and in the two-body collisions approximation. The formalism employed is parallel to that develo-pped by Prigogine and co-workers, so that a comparison may be made with the equations derived by Prigogine and Severne. A complet identity of the results is established at least in the asymptotic limit (t →∞). Finally a different form of the boundary condition is proposed which permits the direct establishment of the identity of the two theories in a much more general form ; it is observed that, in addition, this boundary condition permits a treatment of Bogolubov's theory within the frame of the theory of Prigogine.

We discuss on a simple discrete time spin model how a deterministic classical evolution may be transformed into a stochastic process. Simple averaging over a population of fixed scatterers yields a non-markovian microscopic evolution and is not compatible with a macroscopic description in terms of populations. Coupling each scatter-er to an independent reservoir leads to a Markov process in phase space, which can be projected on a macroscopic birth and death process. Some limiting cases (continuous time interpolation, ...) are considered.