Clausius relation for active particles: what can we learn from fluctuations?

Many kinds of active particles, such as bacteria or active colloids, move in a thermostatted fluid by means of self-propulsion. Energy injected by such a non-equilibrium force is eventually dissipated as heat in the thermostat. Since thermal fluctuations are much faster and weaker than self-propulsion forces, they are often neglected, blurring the identification of dissipated heat in theoretical models. For the same reason, some freedom - or arbitrariness - appears when defining entropy production. Recently three different recipes to define heat and entropy production have been proposed for the same model where the role of self-propulsion is played by a Gaussian coloured noise. Here we compare and discuss the relation between such proposals and their physical meaning. One of these proposals takes into account the heat exchanged with a non-equilibrium active bath: such an "active heat" satisfies the original Clausius relation and can be experimentally verified.Comment: 10 pages, submitted to Entropy journal for the special issue "Thermodynamics and Statistical Mechanics of Small Systems" (see http://www.mdpi.com/journal/entropy/special_issues/small_systems

Dynamic density functional theory versus Kinetic theory of simple fluids

By combining methods of kinetic and density functional theory, we present a description of molecular fluids which accounts for their microscopic structure and thermodynamic properties as well as for the hydrodynamic behavior. We focus on the evolution of the one particle phase space distribution, rather than on the evolution of the average particle density, which features in dynamic density functional theory. The resulting equation can be studied in two different physical limits: diffusive dynamics, typical of colloidal fluids without hydrodynamic interaction, where particles are subject to overdamped motion resulting from the coupling with a solvent at rest, and inertial dynamics, typical of molecular fluids. Finally, we propose an algorithm to solve numerically and efficiently the resulting kinetic equation by employing a discretization procedure analogous to the one used in the Lattice Boltzmann method.Comment: 15 page

Multicomponent Diffusion in Nanosystems

We present the detailed analysis of the diffusive transport of spatially inhomogeneous fluid mixtures and the interplay between structural and dynamical properties varying on the atomic scale. The present treatment is based on different areas of liquid state theory, namely kinetic and density functional theory and their implementation as an effective numerical method via the Lattice Boltzmann approach. By combining the first two methods it is possible to obtain a closed set of kinetic equations for the singlet phase space distribution functions of each species. The interactions among particles are considered within a self-consistent approximation and the resulting effective molecular fields are analyzed. We focus on multispecies diffusion in systems with short-range hard-core repulsion between particles of unequal sizes and weak attractive long-range interactions. As a result, the attractive part of the potential does not contribute explicitly to viscosity but to diffusivity and the thermodynamic properties. Finally, we obtain a practical scheme to solve the kinetic equations by employing a discretization procedure derived from the Lattice Boltzmann approach. Within this framework, we present numerical data concerning the mutual diffusion properties both in the case of a quiescent bulk fluid and shear flow inducing Taylor dispersion.Comment: 19 pages + 5 figure

Kinetic Density Functional Theory: A microscopic approach to fluid mechanics

In the present paper we give a brief summary of some recent theoretical advances in the treatment of inhomogeneous fluids and methods which have applications in the study of dynamical properties of liquids in situations of extreme confinement, such as nanopores, nanodevices, etc. The approach obtained by combining kinetic and density functional methods is microscopic, fully self-consistent and allows to determine both configurational and flow properties of dense fluids. The theory predicts the correct hydrodynamic behavior and provides a practical and numerical tool to determine how the transport properties are modified when the length scales of the confining channels are comparable with the size of the molecules. The applications range from the dynamics of simple fluids under confinement, to that of neutral binary mixtures and electrolytes where the theory in the limit of slow gradients reproduces the known phenomenological equations such as the Planck-Nernst-Poisson and the Smoluchowski equations. The approach here illustrated allows for fast numerical solution of the evolution equations for the one-particle phase-space distributions by means of the weighted density lattice Boltzmann method and is particularly useful when one considers flows in complex geometries.Comment: 14 page

Some conditions under which a uniform space is fine

summary:Let $X$ be a uniform space of uniform weight $\mu$. It is shown that if every open covering, of power at most $\mu$, is uniform, then $X$ is fine. Furthermore, an $\omega _\mu$-metric space is fine, provided that every finite open covering is uniform

Time dependent Ginzburg-Landau equation for an N-component model of self-assembled fluids

We study the time evolution of an N-component model of bicontinuous microemulsions based on a time dependent Ginzburg-Landau equation quenched from an high temperature uncorrelated state to the low temperature phases. The behavior of the dynamical structure factor $\tilde C(k,t)$ is obtained, in each phase, in the framework of the large-$N$ limit with both conserved (COP) and non conserved (NCOP) order parameter dynamics. At zero temperature the system shows multiscaling in the unstructured region up to the tricritical point for the COP whereas ordinary scaling is obeyed for NCOP. In the structured phase, instead, the conservation law is found to be irrelevant and the form $\tilde C(k,t) \sim t^{\alpha / z} f((|k-k_m| t^{1/z})$, with $\alpha=1$ and $z=2$, is obtained in every case. Simple scaling relations are also derived for the structure factor as a function of the final temperature of the thermal bath.Comment: 9 pages,Apste

Steric modulation of ionic currents in DNA translocation through nanopores

Ionic currents accompanying DNA translocation strongly depend on molarity of the electrolyte solution and the shape and surface charge of the nanopore. By means of the Poisson-Nernst-Planck equations it is shown how conductance is modulated by the presence of the DNA intruder and as a result of competing electrostatic and confinement factors. The theoretical results reproduce quantitatively the experimental ones and are summarized in a conductance diagram that allows distinguishing the region of reduced conductivity from the region of enhanced conductivity as a function of molarity and the pore dimension.Comment: 22 pages, 7 figure