Onsager's Principle Research Articles

Hydrodynamic theory of coupled current and magnetization dynamics in spin-textured ferromagnets

We develop the hydrodynamic theory of collinear spin currents coupled to magnetization dynamics in metallic ferromagnets. The collective spin density couples to the spin current through a U(1) Berry-phase gauge field determined by the local texture and dynamics of the magnetization. We determine phenomenologically the dissipative corrections to the equation of motion for the electronic current, which consist of a dissipative spin-motive force generated by magnetization dynamics and a magnetic texture-dependent resistivity tensor. The reciprocal dissipative, adiabatic spin torque on the magnetic texture follows from the Onsager principle. We investigate the effects of thermal fluctuations and find that electronic dynamics contribute to a nonlocal Gilbert damping tensor in the Landau-Lifshitz-Gilbert equation for the magnetization. Several simple examples, including magnetic vortices, helices, and spirals, are analyzed in detail to demonstrate general principles.

Modeling and simulations for molecular scale hydrodynamics of the moving contact line inimmiscible two-phase flows

This paper starts with an introduction to the Onsager principle of minimum energydissipation which governs the optimal paths of deviation and restoration to equilibrium.Then there is a review of the variational approach to moving contact line hydrodynamics.To demonstrate the validity of our continuum hydrodynamic model, numerical results frommodel calculations and molecular dynamics simulations are presented for immiscibleCouette and Poiseuille flows past homogeneous solid surfaces, with remarkableoverall agreement. Our continuum model is also used to study the contact linemotion on surfaces patterned with stripes of different contact angles (i.e. surfaces ofvarying wettability). Continuum calculations predict the stick–slip motion forcontact lines moving along these patterned surfaces, in quantitative agreement withmolecular dynamics simulation results. This periodic motion is tunable throughpattern period (geometry) and contrast in wetting property (chemistry). Theconsequence of stick–slip contact line motion on energy dissipation is discussed.

Extended fluctuation-dissipation theorem for soft matter in stationary flow

For soft matter systems strongly driven by stationary flow, we discuss an extended fluctuation-dissipation theorem (FDT). Beyond the linear-response regime, the FDT for the stress acquires an additional contribution involving the observable that is conjugate to the strain rate with respect to the dissipation function. This extended FDT is evaluated both analytically for Rouse polymers and in numerical simulations for colloidal suspensions. More generally, our results suggest an extension of Onsager's regression principle to nonequilibrium steady states.

Power spectra for both interrupted and perennial aging processes

We study the power spectrum of a random telegraphic noise with the distribution density of waiting times tau given by psi(tau) proportional to 1tau(mu), with mu approximately 2. The condition mu<2 violates the ergodic hypothesis, and in this case the adoption of Wiener-Khintchine (WK) theorem for the spectrum evaluation requires some caution. We study this problem theoretically and numerically and we prove that the power spectrum obeys the prescription S(f)=Kf(eta), with eta=3-mu, namely, the 1f noise lives at border between the ergodic mu>2 and nonergodic mu<2 condition. We study sequences with the finite length L. In the case mu<2 the adoption of WK theorem is made legitimate by two different kinds of truncation effects: the physical and observation-induced effect. In the former case psi(tau) is truncated at tau approximately T(max) and L>>T(max) ensures the condition of interrupted aging. In this case, we find that K is a number independent of L. The latter case, L<<T(max), is more challenging. It was already solved by Margolin and Barkai, who used time asymptotic arguments based on the ergodicity breakdown and obtained K proportional to 1L(2-mu), proving that the out-of-equilibrium nature of the condition mu<2 is signaled by the decrease of K with the increase of L. We use a generalized version of the Onsager principle that leads us to the same conclusion from a somewhat more extended view valid also for the transient out-of-equilibrium case of mu>2. We do not limit our treatment to the time asymptotic case, thereby producing a prediction that accounts for the transition from the 1f(eta) to the 1f(2) regime, recently observed in an experiment on blinking quantum dots. Our theoretical approach allows us to discuss some other recent experiments on molecular intermittent fluorescence and affords indications that should help to assess whether the spectrum is determined by the L<<T(max) or by the L>>T(max) condition.

Electrorheological Fluid Dynamics

We use the Onsager principle to derive a two-phase continuum formulation for the hydrodynamics of the electrorheological (ER) fluid, consisting of dielectric microspheres dispersed in an insulating liquid. Predictions of the theory are in excellent agreement with the experiments. In particular, it is shown that whereas the usual configuration of applied electric field being perpendicular to the shearing direction can lead to shear thinning at high shear rates and thus the loss of ER effect, the interdigitated, alternating electrodes configuration can eliminate the shear-thinning effect.

Fluctuation Relations Without Microreversibility in Nonlinear Transport

In linear transport, the fluctuation-dissipation theorem relates equilibrium current correlations to the linear conductance coefficient. For nonlinear transport, there exist fluctuation relations that rely on Onsager's principle of microscopic reversibility away from equilibrium. However, both theory and experiments have shown deviations from microreversibility in the form of magnetic field asymmetric current-voltage relations. We present novel fluctuation relations for nonlinear transport in the presence of magnetic fields that relate current correlation functions at any order at equilibrium to response coefficients of current cumulants of lower order. We illustrate our results with the example of an electrical Mach-Zehnder interferometer.

A scaling approach to the derivation of hydrodynamic boundary conditions

We show hydrodynamic boundary conditions to be the inherent consequence of the Onsager principle of minimum energy dissipation, provided the relevant effects of the wall potential appear within a thin fluid layer next to the solid wall, denoted the surface layer. The condition that the effect of the surface layer on the bulk hydrodynamics must be independent of its thicknesshis shown to imply a set of consistent ‘scaling relationships’ betweenhand the surface-layer variables/parameters. The use of the scaling relations, in conjunction with the surface-layer equations of motion derived from the Onsager principle, directly leads to the hydrodynamic boundary conditions. We demonstrate the surface-layer scaling process both physically and mathematically, and relate the parameters of the boundary conditions to those in the surface-layer equations of motion. In spatial regions outside the surface layer, equivalence between the use of surface-layer dynamics and boundary conditions is numerically demonstrated for Couette flows. As an application of the present approach, we derive the liquid-crystal hydrodynamic boundary conditions in which the rotational and translational dynamics are coupled.

Nonequilibrium nanothermodynamics

Entropy production for a system outside the thermodynamic limit is formulated using Hill's nanothermodynamics, in which a macroscopic ensemble of such systems is considered. The external influence of the environment on the average nanosystem is connected to irreversible work with an explicit formula based on the Jarzynski equality. The entropy production retains its usual form as a sum of products of fluxes and forces and Onsager's symmetry principle is proven to hold for the average nanosystem, if it is assumed to be valid for the macroscopic ensemble, by two methods. The first one provides expressions that relate the coefficients of the two systems. The second gives a general condition for a system under an external force to preserve Onsager's symmetry.

Onsager Principle and Electrorheological Fluid Dynamics

We present the formulation of a two-phase, electrical-hydrodynamic model for the description of electrorheological fluid dynamics, based on the Onsager principle of minimum energy dissipation. By considering the energetics of (induced) dipole-dipole interaction between the solid particles in terms of a field variable n(� x ), we employ the Onsager principle to derive the relevant coupled hydrodynamic equations, together with a continuity equation for n(� x ). Numerical solution of the relevant equations yields predictions that display very realistic behaviors as seen experimentally. In particular, we show that while the predicted results have features that resemble Bingham fluids, there can be important differences. For example, the yield stress obtained by extrapolating the shear rate to zero is 30-40% lower than that obtained from the maximum of the stress-strain relation. Moreover, for the conventional electrode configuration where the field is perpendicular to the shearing direction, there is very clear shearing-thinning effect that has been seen experimentally.

Non-reciprocity of Faraday rotation in gyrotropic crystals

Abstract It is shown that, under the conditions of coexisting natural optical activity and non-zero linear optical birefringence, reversal of the light wave vector sign can result in changing angle of Faraday rotation. Keywords: natural optical activity, Faraday rotation, magnetogyration, non-reciprocity PACS: 33.55.Ad, 78.20.Ls, 78.20.Ek, 78.20.Fm UDC: 535.37 Introduction The effect of additional optical rotation observed earlier in a number of absorbing non-centrosymmetric crystals under the influence of external magnetic field [1–3], which has been explained as a magnetogyration (MG) [4–6], is usually distinguished from the Faraday rotation (FR) via reversing the wave vector of light or rotating a crystal sample by 180 o around the axis perpendicular to the optic axis of the crystal. In relation to this problem, it is worth noticing that the MG as a spatial dispersion effect induced by magnetic field should not, in principle, manifest itself as an optical rotation. Indeed, according to the known Onsager principle, it should lead to changes in the real part of the dielectric permittivity (or the refractive indices), as a result of the so-called ‘

HYDRODYNAMIC BOUNDARY CONDITION AT THE FLUID-SOLID INTERFACE

While the no-slip boundary condition (no relative motion at the fluid-solid interface) has been universally accepted as a cornerstone of hydrodynamics, it was known for some time that it is incompatible with the moving contact line, defined as the motion of the line of intersection of the immiscible (two phase) fluid-fluid interface with the solid wall. By employing Onsager's principle of minimum energy dissipation, we show in this work that a continuum hydrodynamics, comprising the equations of motion as well as the relevant boundary conditions, can be obtained which resolves the moving contact line problem. Our derivation reveals that just as other dissipative system dynamics, the fluid-solid interfacial boundary condition should be consistent with the framework of linear response theory. Implications of our results are discussed.

Interface Instability under Forced Displacements

By applying linear response theory and the Onsager principle, the power (per unit area) needed to make a planar interface move with velocity V is found to be equal to V2/ μ, μ a mobility coefficient. To verify such a law, we study a one dimensional model where the interface is the stationary solution of a non local evolution equation, called an instanton. We then assign a penalty functional to orbits which deviate from solutions of the evolution equation and study the optimal way to displace the instanton. We find that the minimal penalty has the expression V2/ μ only when V is small enough. Past a critical speed, there appear nucleations of the other phase ahead of the front, their number and location are identified in terms of the imposed speed.

Onsager's coefficients and diffusion laws—a Monte Carlo study

For a numerical description of multicomponent diffusion processes, the coefficients of the Onsager diffusion matrix are needed. We compare a number of models relating these parameters to experimentally accessible quantities, such as tracer diffusion coefficients. Since these models present different levels of approximation, we investigate the differences in Onsager parameters when they are determined from tracer diffusion. Moreover, we study an ideal solution alloy by Monte Carlo methods to determine the Onsager coefficients directly and using the model assumptions. Measuring atomic fluxes and site fraction gradients, our simulation method is more closely related to a real physical experiment than the usual simulation method of generalized Einstein equations. Onsager's variation principle for the calculation of the kinetic coefficients is extended and it is shown that a reasonable description, even of a simple alloy system, requires consideration of a non-diagonal dissipation matrix in the derivation of the diffusion equations.

Frequency-dependent velocity and vorticity fields of electro-osmotic flow in a closed-end cylindrical microchannel

The frequency-dependent electro-osmotic flow in closed-end cylindrical microchannels is analyzed in this study. A dynamic ac electro-osmotic flow field is obtained analytically by solving the Navier–Stokes equation using the Green function formulation in combination with a complex variable approach. Onsager's principle of reciprocity is demonstrated to be valid for transient and ac electro-osmotic flow. The effect of a frequency-dependent ac electric field on the oscillating electro-osmotic flow is studied. The induced pressure gradient is analyzed under the effects of the channel dimension and the frequency of electric field. Based on the Stokes second problem, the solution of the slip velocity approximation is presented for comparison with the results obtained from the analytical solution developed in this study. In addition, the expression for the electro-osmotic vorticity field is derived, and the characteristic of the vorticity field in ac electro-osmotic flow is discussed.

Non-Poisson processes: regression to equilibrium versus equilibrium correlation functions

We study the response to perturbation of non-Poisson dichotomous fluctuations that generate super-diffusion. We adopt the Liouville perspective and with it a quantum-like approach based on splitting the density distribution into a symmetric and an anti-symmetric component. To accomodate the equilibrium condition behind the stationary correlation function, we study the time evolution of the anti-symmetric component, while keeping the symmetric component at equilibrium. For any realistic form of the perturbed distribution density we expect a breakdown of the Onsager principle, namely, of the property that the subsequent regression of the perturbation to equilibrium is identical to the corresponding equilibrium correlation function. We find the directions to follow for the calculation of higher-order correlation functions, an unsettled problem, which has been addressed in the past by means of approximations yielding quite different physical effects.

Heat transfer in the Knudsen layer.

A concept of the surface heat conductivity determining a heat transfer in the Knudsen layer was introduced. It has the same order with respect to the Knudsen number as the bulk heat transfer and must be taken into account in practical calculations. Using the Onsager principle the coefficient of the surface heat conductivity was related to the thermal slip coefficient.

On energy transfer and generation of an electric current in the vicinity of an electrode dipped in an electrolyte and strongly heated by a current passing through it

Processes occurring when a metal electrode dipped in an electrolyte is heated by intense evaporation of the electrolyte are considered in terms of a physically rigorous model. Based on the Onsager principle of least energy dissipation rate in nonequilibrium processes, the fractions of thermal energy that are spent on heating and evaporating the electrolyte and on heating the vapor are found. The energy is released within the vapor-gas sheath when an electric current flows between the electrode and electrolyte surface. It is found that the electrolyte vapor temperature exceeds 1300 K. Analytical expressions are derived for the vapor-gas sheath thickness, the electrolyte vapor pressure, and the velocity of the vapor escaping the discharge zone. It is shown that field evaporation of thermally activated negative ions from the electrolyte surface cannot provide an electric current with densities found in experiments but is responsible for the generation of free electrons near the electrolyte surface. These electrons arise when the ions decay via collisions with excited molecules.

Frequency-dependent laminar electroosmotic flow in a closed-end rectangular microchannel

This article presents an analysis of the frequency- and time-dependent electroosmotic flow in a closed-end rectangular microchannel. An exact solution to the modified Navier–Stokes equation governing the ac electroosmotic flow field is obtained by using the Green's function formulation in combination with a complex variable approach. An analytical expression for the induced backpressure gradient is derived. With the Debye–Hückel approximation, the electrical double-layer potential distribution in the channel is obtained by analytically solving the linearized two-dimensional Poisson–Boltzmann equation. Since the counterparts of the flow rate and the electrical current are shown to be linearly proportional to the applied electric field and the pressure gradient, Onsager's principle of reciprocity is demonstrated for transient and ac electroosmotic flows. The time evolution of the electroosmotic flow and the effect of a frequency-dependent ac electric field on the oscillating electroosmotic flow in a closed-end rectangular microchannel are examined. Specifically, the induced pressure gradient is analyzed under effects of the channel dimension and the frequency of electric field. In addition, based on the Stokes second problem, the solution of the slip velocity approximation is presented for comparison with the results obtained from the analytical scheme developed in this study.

Generalized master equation via aging continuous-time random walks.

We discuss the problem of the equivalence between continuous-time random walk (CTRW) and generalized master equation (GME). The walker, making instantaneous jumps from one site of the lattice to another, resides in each site for extended times. The sojourn times have a distribution density psi(t) that is assumed to be an inverse power law with the power index micro. We assume that the Onsager principle is fulfilled, and we use this assumption to establish a complete equivalence between GME and the Montroll-Weiss CTRW. We prove that this equivalence is confined to the case where psi(t) is an exponential. We argue that is so because the Montroll-Weiss CTRW, as recently proved by Barkai [E. Barkai, Phys. Rev. Lett. 90, 104101 (2003)], is nonstationary, thereby implying aging, while the Onsager principle is valid only in the case of fully aged systems. The case of a Poisson distribution of sojourn times is the only one with no aging associated to it, and consequently with no need to establish special initial conditions to fulfill the Onsager principle. We consider the case of a dichotomous fluctuation, and we prove that the Onsager principle is fulfilled for any form of regression to equilibrium provided that the stationary condition holds true. We set the stationary condition on both the CTRW and the GME, thereby creating a condition of total equivalence, regardless of the nature of the waiting-time distribution. As a consequence of this procedure we create a GME that is a bona fide master equation, in spite of being non-Markov. We note that the memory kernel of the GME affords information on the interaction between system of interest and its bath. The Poisson case yields a bath with infinitely fast fluctuations. We argue that departing from the Poisson form has the effect of creating a condition of infinite memory and that these results might be useful to shed light on the problem of how to unravel non-Markov quantum master equations.

Minimum Dissipation Principle in Stationary Non-Equilibrium States

We generalize to non equilibrium states Onsager's minimum dissipation principle. We also interpret this principle and some previous results in terms of optimal control theory. Entropy production plays the role of the cost necessary to drive the system to a prescribed macroscopic configuration.