A universal phenomenological approach to study evolution of long-wave fluctuations caused by the external random force is developed. The Furutzu–Novikov theorem is generalized for non-Gaussian processes. General kinetic and hydrodynamic equations that include the effect of long-wave...

Nonlinear equations governing the relaxation of some macroscopic quantities, a(r,t) are derived using Kubo's response theory, in isolated inhomogeneous systems. The resulting equations contain microcanonical time correlation functions. It is shown how to express these in terms of arbitrary...

The Hamilton equations for a Brownian particle involve its mass as a large parameter. As a consequence its motion is relatively slow and the fast motion of the surrounding fluid molecules can be eliminated by the standard method of eliminating fast variables. The result is equivalent to the...

We construct a closed-form expression for the self-diffusion constant, D, for a hard-sphere particle whose mass and radius are large compared to the corresponding bath-particle quantities. The expression yields the Stokes-Einstein law at high bath-particle densities and the Boltzmann form for...

The paper proposes a new approach to describe fluctuations of reversible chemical reactions in closed systems. The deterministic rate laws are cast into the form of nonlinear Onsager type closed laws. By means of nonlinear transport theory a Fokker-Planck equation describing the stochastic...

The Mori formalism is used to study generalized transport coefficients in two dimensions. All finite multilinear products of the single particle density and momentum density comprise the set of the variables in the calculation of the self-diffusion coefficient. A self-consistent equation, which...

We have derived, starting from the Liouville equation and using projection operators, the three-dimensional Langevin and Fokker-Planck equations for the time dependence of the momenta and position of two Brownian particles of mass M interacting with a harmonic potential (i.e., a harmonic...

The coupled diffusion equations recently proposed by Tokuyama for concentrated hard-sphere suspensions are numerically solved, starting from nonequilibrium initial configurations. The most important feature of those equations is that the self-diffusion coefficient DS(Φ) becomes zero at the...

The convergence properties of the integral corresponding to the three-body cyclic collisions in the two-dimensional density expansion of transport coefficients are investigated. It is shown exactly that the integral considered by Oppenheim et al. and by Eu diverges logarithmically in the...

Local order effects on the dynamical properties of critical fluids are taken into account by introducing a new slowly varying tensorial quantity which is related to the angular momentum of a group of correlated molecules. The theory is applied to an analysis of ultrasonic and light scattering...