The Onsager reciprocity relation and generalized efficiency of a thermal Brownian motor

Based on a general model of Brownian motors, the Onsager coefficients and generalized efficiency of a thermal Brownian motor are calculated analytically. It is found that the Onsager reciprocity relation holds and the Onsager coefficients are not affected by the kinetic energy change due to the particle's motion. Only when the heat leak in the system is negligible can the determinant of the Onsager matrix vanish. Moreover, the influence of the main parameters characterizing the model on the generalized efficiency of the Brownian motor is discussed in detail. The characteristic curves of the generalized efficiency varying with these parameters are presented, and the maximum generalized efficiency and the corresponding optimum parameters are determined. The results obtained here are of general significance. They are used to analyze the performance characteristics of the Brownian motors operating in the three interesting cases with zero heat leak, zero average drift velocity or a linear response relation, so that some important conclusions in current references are directly included in some limit cases of the present paper.     

Onset of Rayleigh-Bénard convection in a ternary liquid system and the Onsager law with generalized thermal diffusion

For the ternary system isopropanol-ethanol-water, a model was proposed to estimate the cross diffusion coefficients from measurements of the critical parameters for the onset of Rayleigh-Bénard convection, together with the consideration of the reciprocity laws of Onsager. Among the three forms of the chemical potentials used, not a single chemical potential was found to provide a correlation between the Onsager laws and the experimental data. The present study shows that consideration of a generalized thermal diffusion term taking account of all components is adequate to estimate quantitative values of the cross diffusion coefficients.     

Electron-phonon entrainment, thermodynamic effects, and the thermal conductivity of degenerate conductors

A method is proposed for calculating the kinetic coefficients of degenerate conductors that takes into account in a self-consistent way the mutual influence of the nonequilibrium state of the electron and phonon subsystems. The calculated expressions for the kinetic coefficients satisfy Onsager symmetry relations. The influence of the nonequilibrium character of the electron-phonon subsystem on the electrical conductivity, thermal voltage, and electronic thermal conductivity is analyzed. Fiz. Tverd. Tela (St. Petersburg) 41, 1753–1762 (October 1999)     

Work distribution function for a Brownian particle driven by a nonconservative force

We derive the distribution function of work performed by a harmonic force acting on a uniformly dragged Brownian particle subjected to a rotational torque. Following the Onsager and Machlup’s functional integral approach, we obtain the transition probability of finding the Brownian particle at a particular position at time t given that it started the journey from a specific location at an earlier time. The difference between the forward and the time-reversed form of the generalized Onsager-Machlup’s Lagrangian is identified as the rate of medium entropy production which further helps us develop the stochastic thermodynamics formalism for our model. The probability distribution for the work done by the harmonic trap is evaluated for an equilibrium initial condition. Although this distribution has a Gaussian form, it is found that the distribution does not satisfy the conventional work fluctuation theorem.     

Charged Brownian particles: Kramers and Smoluchowski equations and the hydrothermodynamical picture

We consider a charged Brownian gas under the influence of external and non-uniform electric, magnetic and mechanical fields, immersed in a non-uniform bath temperature. With the collision time as an expansion parameter, we study the solution to the associated Kramers equation, including a linear reactive term. To the first order we obtain the asymptotic (overdamped) regime, governed by transport equations, namely: for the particle density, a Smoluchowski-reactive like equation; for the particle’s momentum density, a generalized Ohm’s-like equation; and for the particle’s energy density, a Maxwell-Cattaneo-like equation. Defining a nonequilibrium temperature as the mean kinetic energy density, and introducing Boltzmann’s entropy density via the one particle distribution function, we present a complete thermohydrodynamical picture for a charged Brownian gas. We probe the validity of the local equilibrium approximation, Onsager relations, variational principles associated to the entropy production, and apply our results to: carrier transport in semiconductors, hot carriers and Brownian motors. Finally, we outline a method to incorporate non-linear reactive kinetics and a mean field approach to interacting Brownian particles.     

Brownian refrigerator

Onsager symmetry implies that a Brownian motor, driven by a temperature gradient, will also perform a refrigerator function upon loading. We analytically calculate the corresponding heat flow for an exactly solvable microscopic model and compare it with molecular dynamics simulations.     

Multiple branches of ordered states of polymer ensembles with the Onsager excluded volume potential

We study the branches of equilibrium states of rigid polymer rods with the Onsager excluded volume potential in two-dimensional space. Since the probability density and the potential are related by the Boltzmann relation at equilibrium, we represent an equilibrium state using the Fourier coefficients of the Onsager potential. We derive a non-linear system for the Fourier coefficients of the equilibrium state. We describe a procedure for solving the non-linear system. The procedure yields multiple branches of ordered states. This suggests that the phase diagram of rigid polymer rods with the Onsager potential has a more complex structure than that with the Maier-Saupe potential. A study of free energy indicates that the first branch of ordered states is stable while the subsequent branches are unstable. However, the instability of the subsequent branches does not mean they are not interesting. Each of these unstable branches, under certain external potential, can be made metastable, and thus may be observed.     

Evaluation of the translational and rotational diffusion coefficients of a cubic particle (for the application to Brownian dynamics simulations)

By estimating the force and torque acting on the cube for the two cases of a uniform flow field and a rotational flow field, we have discussed whether or not there is a coupling between the translational and the rotational motion. From the characteristics of the friction coefficients, we may understand that there is no coupling between the translation motion and the rotational motion in the situation of the Reynolds number being sufficiently smaller than unity. In contrast, in the case of a non-slow flow field with the Reynolds number larger than unity, the coupling characteristics of the motion of a cube is certainly recognised and therefore the interaction with the ambient fluid is characterised by a variety of friction coefficients including friction coefficients that relate the forces acting on the cube to the angular velocities of the rotational motion. Hence, the employment of these translational and rotational diffusion coefficients for a cube enables the implementation of Brownian dynamics simulations for a suspension composed of cubic particles in order to analyse the dynamic characteristics of a cubic particle suspension.

Highlights

1. We have considered a flow problem around a cube in order to numerically clarify the characteristics of the translational and rotational friction or diffusion coefficients.

2. In a slow flow field the motion of the cube need only to be characterised by two friction coefficients, i.e. the translational and rotational friction coefficients.

3. In the case of a non-slow flow field, the coupling characteristics between the translational motion and the rotational motion are recognised.

4. Employment of these diffusion coefficients enables the implementation of Brownian dynamics simulations for a suspension composed of cubic particles.

     

Field-driven dynamical demixing of binary mixtures

ABSTRACT

We consider mixtures of two species of spherical colloidal particles that differ in their Stokes coefficients, but are otherwise identical, in the presence of an external field. Since the particle–particle and particle–field interactions are the same for both species, they are completely mixed in the thermodynamic limit in the presence of any static field. Here, we combine Brownian dynamics and dynamic density functional theory of fluids to show that for sufficiently large differences in the Stokes coefficients of the particles (and corresponding differences in their mobilities) dynamical demixing is observed. These demixed states are transient but, under certain conditions, packing effects compromise the relaxation towards the thermodynamic states and the lifetime of the demixed phases increases significantly.     

Rayleigh decay of a highly charged bubble in a dielectric liquid

Proceeding from the Onsager principle of minimum energy dissipation, we find the dimensions, charges, and total number of daughter bubbles emitted during an instability of a highly charged bubble in a dielectric liquid. Zh. Tekh. Fiz. 69, 11–15 (February 1999)     

Onsager-Zerlegung und generalisierte Langevin-Theorie für ein Brownsches Teilchen in der harmonischen Kette

To illustrate the so-called Onsager separability of dynamic correlation functions (which is fundamental to the Statistical Mechanics of phenomenological processes) we consider the exact generalized Langevin equation for the momentum of a Brownian particle in a harmonic chain. The time dependence of the Langevin force and its dynamic autocorrelation (the after effect kernel) are calculated and shown to have no hydrodynamic part—in contrast to the particle's momentum correlation.     

Archimedean-like colloidal tilings on substrates with decagonal and tetradecagonal symmetry

Two-dimensional colloidal suspensions subjected to laser interference patterns with decagonal symmetry can form an Archimedean-like tiling phase where rows of squares and triangles order aperiodically along one direction (J. Mikhael et al., Nature 454, 501 (2008)). In experiments as well as in Monte Carlo and Brownian dynamics simulations, we identify a similar phase when the laser field possesses tetradecagonal symmetry. We characterize the structure of both Archimedean-like tilings in detail and point out how the tilings differ from each other. Furthermore, we also estimate specific particle densities where the Archimedean-like tiling phases occur. Finally, using Brownian dynamics simulations we demonstrate how phasonic distortions of the decagonal laser field influence the Archimedean-like tiling. In particular, the domain size of the tiling can be enlarged by phasonic drifts and constant gradients in the phasonic displacement. We demonstrate that the latter occurs when the interfering laser beams are not ideally adjusted.     

Spin Operator Matrix Elements in the Superintegrable Chiral Potts Quantum Chain

We derive spin operator matrix elements between general eigenstates of the superintegrable ℤ _N -symmetric chiral Potts quantum chain of finite length. Our starting point is the extended Onsager algebra recently proposed by Baxter. For each pair of spaces (Onsager sectors) of the irreducible representations of the Onsager algebra, we calculate the spin matrix elements between the eigenstates of the Hamiltonian of the quantum chain in factorized form, up to an overall scalar factor. This factor is known for the ground state Onsager sectors. For the matrix elements between the ground states of these sectors we perform the thermodynamic limit and obtain the formula for the order parameters. For the Ising quantum chain in a transverse field (N=2 case) the factorized form for the matrix elements coincides with the corresponding expressions obtained recently by the Separation of Variables method.     

Interdiffusion and thermotransport in Ni–Al liquid alloys

In this paper, we present extensive self-consistent results of molecular dynamics (MD) simulations of diffusion and thermotransport properties of Ni–Al liquid alloys. We develop a new formalism that allows easy connection between results of the MD simulations and the real experiments. In addition, this formalism can be extended to the case of ternary and higher component liquid alloys. We focus on the temperature and composition dependence of the self-diffusion coefficients, interdiffusion coefficients, thermodynamic factor, Manning factor and the reduced heat of transport. The two latter quantities both represent measures of the off-diagonal Onsager phenomenological coefficients. The Manning factor and the reduced heat of transport can be related to experimentally obtainable quantities provided the thermodynamic factor is available. The simulation results for the reduced heat of transport show that for all compositions, in the presence of a temperature gradient, Ni tends to migrate to the cold end. This is in agreement with an available experimental study for a Ni_21.5Al_78.5 melt (only qualitative result is available so far).     

Zur phänomenologischen linearen Antwort von Onsager-Systemen

The Onsager separability of time-dependent correlation functions is used to construct the linearphenomenological response of large physical systems to an external perturbation. Both the classical and the quantum case are included. Simple electrical networks and the Brownian particle in the harmonic chain are treated as examples.     

Comment on “Role of the velocity frame of reference in thermodiffusion in liquid mixtures” by M. Eslamian,C.G. Jiang and M.Z. Saghir

We analyze the material transport equations (MTE) derived by Eslamian and co-authors and address the criticism expressed regarding the approach formulated in our previous work. In doing so, we show that the MTE formulated by Eslamian and co-authors are valid only in closed stationary non-isothermal systems in combination with the restrictions on the Onsager coefficients formulated in our work which is criticized, and that for non-stationary systems the approach we took can be used.     

Decoherence induced by zero-point fluctuations in quantum Brownian motion

We show a completely analytical approach to the decoherence induced by a zero temperature environment on a Brownian test particle. We consider an Ohmic environment bilinearly coupled to an oscillator and compute the master equation. From diffusive coefficients, we evaluate the decoherence time for the usual quantum Brownian motion and also for an upside-down oscillator, as a toy model of a quantum phase transition.