Inertial effects in non-equilibrium thermodynamics

We discuss inertial effects in systems outside equilibrium within the frame work of nonequilibrium thermodynamics. By introducing a Gibbs equation in w hich the entropy depends on the probability density, we are able to describ e a system of Brownian particles immersed in a heat bath in both inertial a nd diffusion regimes. In the former, a relaxation equation for the diffusio n current is obtained whereas in the latter we recover Fick's law. Our appr oach, which uses the elements of the theory of internal degrees of freedom, constitutes the mesoscopic version of a previous analysis which takes into account the kinetic energy of diffusion. (C) 1999 Elsevier Science B.V. Al l rights reserved.