Twenty-five years of non-equilibrium statistical mechanics: Towards a better understanding of dense fluids

Abstract

A survey is given of some of the new insights that have emerged over the last 25 years in the physics of dense non-equilibrium fluids: atomic liquids as well as concentrated colloidal suspensions. First a brief discussion of some previous developments is given: the non-existence of a density expansion of the transport coefficients; the existence of general expressions for the transport coefficients for a fluid in terms of average current time-autocorrelation functions in equilibrium and the slow decay of the latter due to mode-coupling by vortex-diffusion, a new mechanism of diffusion leading to the long time tails. Next, very long range correlations, also due to mode-coupling, in non-equilibrium fluids subject to a temperature gradient and their experimental detection by light or by microwave scattering are discussed. Also, a reinterpretation of the neutron spectra of dense fluids in equilibrium is given in terms of effective fluid eigenmodes and cage-diffusion, the most important diffusion process in dense fluids. Then some recent work on Lattice Gas Cellular Automata and a new connection between transport coefficients and Lyapunov exponents are briefly mentioned. Finally, a far going analogy between the self-diffusion coefficient and the viscosity of atomic liquids and those of concentrated colloidal suspensions is discussed, based on the similarity of Newtonian and Brownian dynamics on long time scales and that of the cage-diffusion processes in both systems. Very similar expressions for the viscosity of these two fluid systems, based on cage-diffusion, are compared with recent experiments.