We use a local equilibrium approximation to study a system described by a nonlinear Fokker-Planck equation. It is shown that the approximation leads to renormalized transport equations and to a spectral density which are in good agreement with those obtained by more cumbersome methods.

It is shown that the three-particle kinetic operator for inhomogeneous gases obtained using Prigogine's method and the matrix representation of the Liouville equation introduced by Balescu is equivalent to the corresponding expression derived by Choh and Uhlenbeck using Bogolubov's method. Both...

An analogue Fokker-Planck equation also referred to as the Fokker-Planck-Klein-Kramers equation for N interacting Brownian particles in a fluid is derived using the matrix representation of the Liouville equation in the general theory of irreversible processes developed by the Brussels school....

The Fokker-Planck equation is obtained using the matrix representation of the Liouville equation introduced by Balescu in the general theory of irreversible processes developed by the Brussels group. It is shown that the phenomenological equation is valid when the mass and density of the...

The dynamics of a model introduced by Kometani and Shimizu is studied in the limit of the number of particles going to infinity. In addition to the cumulant expansion already considered by Desai and Zwanzig, we study the low diffusion constant approximation. Both methods present difficulties...

We derive fluctuation renormalized transport equations for the averages position and velocity of a weakly nonlinear Duffing oscillator. We take the nonlinearity as the expansion parameter and use a modification of the van Kampen expasion method. Also, we study the spectral density of the...

The evolution operator in the correlation-patterns representation is studied in the linear approximation. The linearized master evolution equations satisfied by the vacuum and the correlations are derived. The equations are applicable to inhomogeneous systems. The structure of the introduced...

Through an analysis of the expression of the autocorrelation function of the velocities in the matrix representation, an identification is made of all the matrix elements which lead to the so-called t or ϵ explicit divergence. The terms in the expansion can be easily summed and as a result the...

The influence of a nonconservative force proportional to the velocity acting on a system described by the Boltzmann equation is analyzed. When this force is the only external action on the system, an H-theorem is proved, showing that the distribution function tends towards a Maxwellian with a...