We analyze the diffusion of a Brownian particle in a fluid under stationary flow. By using the scheme of nonequilibrium thermodynamics in phase space, we obtain the Fokker-Planck equation that is compared with others derived from the kinetic theory and projector operator techniques. This equation exhibits violation of the fluctuation-dissipation theorem. By implementing the hydrodynamic regime described by the first moments of the nonequilibrium distribution, we find relaxation equations for the diffusion current and pressure tensor, allowing us to arrive at a complete description of the system in the inertial and diffusion regimes. The simplicity and generality of the method we propose makes it applicable to more complex situations, often encountered in problems of soft-condensed matter, in which not only one but more degrees of freedom are coupled to a nonequilibrium bath.

We propose a simple and general model accounting for the dependence of the viscosity of a hard sphere suspension at arbitrary volume fractions. The model constitutes a continuummedium description based on a recursive-differential method that assumes a hierarchy of relaxation times. Geometrical information of the system is introduced through an effective volume fraction that approaches the usual filling fraction at low concentrations and becomes one at maximum packing. The agreement of our expression for the viscosity with experiments at low-and high-shear rates and in the high-frequency limit is remarkable for all volume fractions.

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A thermodynamics for systems at a stationary state is formulated. It is based upon the assumption of the existence of local equilibrium in phase space which enables one to interpret the probability density and its conjugated nonequilibrium chemical potential as mesoscopic thermodynamic variables. The probability current is obtained from the entropy production related to the probability diffusion process and leads to the formulation of the Fokker-Planck equation. For the case of a gas of Brownian particles under steady flow in the dilute and concentrated regimes we derive nonequilibrium equations of state.

Transmitter exocytosis from the neuronal soma is evoked by brief trains of high frequency electrical activity and continues for several minutes. Here we studied how active vesicle transport towards the plasma membrane contributes to this slow phenomenon in serotonergic leech Retzius neurons, by combining electron microscopy, the kinetics of exocytosis obtained from FM1-43 dye fluorescence as vesicles fuse with the plasma membrane, and a diffusion equation incorporating the forces of local confinement and molecular motors. Electron micrographs of neurons at rest or after stimulation with 1 Hz trains showed cytoplasmic clusters of dense core vesicles at 1.5±0.2 and 3.7±0.3 µm distances from the plasma membrane, to which they were bound through microtubule bundles. By contrast, after 20 Hz stimulation vesicle clusters were apposed to the plasma membrane, suggesting that transport was induced by electrical stimulation. Consistently, 20 Hz stimulation of cultured neurons induced spotted FM1-43 fluorescence increases with one or two slow sigmoidal kinetics, suggesting exocytosis from an equal number of vesicle clusters. These fluorescence increases were prevented by colchicine, which suggested microtubule-dependent vesicle transport. Model fitting to the fluorescence kinetics predicted that 52–951 vesicles/cluster were transported along 0.60–6.18 µm distances at average 11–95 nms−1 velocities. The ATP cost per vesicle fused (0.4–72.0), calculated from the ratio of the ΔGprocess/ΔGATP, depended on the ratio of the traveling velocity and the number of vesicles in the cluster. Interestingly, the distance-dependence of the ATP cost per vesicle was bistable, with low energy values at 1.4 and 3.3 µm, similar to the average resting distances of the vesicle clusters, and a high energy barrier at 1.6–2.0 µm. Our study confirms that active vesicle transport is an intermediate step for somatic serotonin exocytosis by Retzius neurons and provides a quantitative method for analyzing similar phenomena in other cell types.