Superstatistics of Brownian motion: A comparative study

The dynamics of temperature fluctuations of a gas of Brownian particles in local equilibrium with a nonequilibrium heat bath, are described using an approach consistent with Boltzmann-Gibbs statistics (BG). We use mesoscopic nonequilibrium thermodynamics (MNET) to derive a Fokker-Planck equation for the probability distribution in phase space including the local intensive variables fluctuations. We contract the description to obtain an effective probability distribution (EPD) from which the mass density, van Hove's function and the dynamic structure factor of the system are obtained. The main result is to show that in the long time limit the EPD exhibits a similar behavior as the superstatistics distribution of nonextensive statistical mechanics (NESM), therfore implying that the coarse-graining procedure is responsible for the so called nonextensive effects.Comment: 14 pages,5 figure

A Nonequilibrium Thermodynamic Approach to Generalized Statistics for Brownian Motion

We analyze the dynamics of a Brownian gas in contact with a heat bath in which large temperature fluctuations occur. There are two distinct time scales present, one describes the decay of the fluctuations in the temperature and the other one is associated with the establishment of local equilibrium. Although the gas has reached local equilibrium, there exist large fluctuations in an intensive parameter (temperature) which break the thermodynamic equilibrium with the heat bath. Thus the decay of the fluctuations in the intensive parameter is larger than the characteristic time for the establishment of local equilibrium. We show that the dynamics of such large and intensive fluctuations may be described by adopting a nonequilibrium thermodynamics approach with an adequate formulation of local equilibrium. A coarsening procedure is then used to contract the space of mesoscopic variables needed to describe the dynamics of the gas and the extensive character of the description is lost. This procedure allows us to derive an effective Maxwell-Boltzmann factor (EMBF) for the Brownian gas, as has been recently proposed in the literature. Furthermore, we use this local equilibrium distribution and an entropy functional to derive a nonequilibrium probability distribution and a hydrodynamic description for the Brownian gas which contains fluctuating transport coefficients. The ensuing description is nonextensive and our analysis shows that the coarse-graining procedure is responsible for the nonextensivity property.Comment: 13 page

Finite-size effects in intracellular microrheology

We propose a model to explain finite-size effects in intracellular microrheology observed in experiments. The constrained dynamics of the particles in the intracellular medium, treated as a viscoelastic medium, is described by means of a diffusion equation in which interactions of the particles with the cytoskeleton are modelled by a harmonic force. The model reproduces the observed power-law behavior of the mean-square displacement in which the exponent depends on the ratio between particle-to-cytoskeleton-network sizes.Comment: 6 pages 2 figures. To appear in the Journal of Chemical Physic

Mesoscopic constitutive relations for dilute polymer solutions

A novel approach to the dynamics of dilute solutions of polymer molecules under flow conditions is proposed by applying the rules of mesoscopic nonequilibrium thermodynamics (MNET). The probability density describing the state of the system is taken to be a function of the position and velocity of the molecules, and on a local vector parameter accounting for its deformation. This function obeys a generalized Fokker-Planck equation, obtained by calculating the entropy production of the system, and identifying the corresponding probability currents in terms of generalized forces. In simple form, this coarse-grained description allows one to derive hydrodynamic equations where molecular deformation and diffusion effects are coupled. A class of non-linear constitutive relations for the pressure tensor are obtained. Particular models are considered and compared with experiments.Comment: To be published in Physica A (16 pages, 2 figures

The transition to irreversibility in sheared suspensions: An analysis based on a mesoscopic entropy production

We study the shear-induced diffusion effect and the transition to irreversibility in suspensions under oscillatory shear flow by performing an analysis of the entropy production associated to the motion of the particles. We show that the Onsager coupling between different contributions to the entropy production is responsible for the scaling of the mean square displacement on particle diameter and applied strain. We also show that the shear-induced effective diffusion coefficient depends on the volume fraction and use Lattice-Boltzmann simulations to characterize the effect through the power spectrum of particle positions for different Reynolds numbers and volume fractions. Our study gives a thermodynamic explanation of the the transition to irreversibility through a pertinent analysis of the second law of thermodynamics.Comment: 17 pages, 3 figures, paper submitted tp phys rev

The rheology of hard sphere suspensions at arbitrary volume fractions: An improved differential viscosity model

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 continuum-medium 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.Comment: 16 pages, 6 figures, submitte