Onsager Relations Research Articles

Nonequilibrium steady-state response of a nematic liquid crystal under simple shear flow and electric fields

The effect of a dc electric field on the response of a nematic liquid crystal under shear flow has been investigated by measuring the shear stress response to an ac electric field used as a probe. It was found that both the first- and second-order responses do not vanish at high frequencies, but have constant nonzero values. The experimental results are in good agreement with calculations based on the Ericksen-Leslie theory. The role of the Parodi relation (which is derived from the Onsager reciprocal relation) in the stress response is discussed.

Onsager's symmetry relation and the residual parallel Reynolds stress in a magnetized plasma with electrostatic turbulence

The physics of the residual parallel Reynolds stress in a rotating plasma with electrostatic turbulence is explicitly identified by using the transport formulation of the gyrokinetic turbulence. It is clarified that the residual stress consists of four terms, among which are the cross terms due to the pressure gradient and the temperature gradient and the terms related to the turbulent acceleration impulse and the turbulent heating rate. The last two terms are identified for the first time, and are shown to cause analogous residual term in the heat flux. Meanwhile, the transport matrix reveals diffusion in the phase space. The transport matrix is demonstrated to satisfy the Onsager's symmetry relation.

Thermoelectric transport properties through a single-walled zig–zag carbon nanotube side coupled to a correlated quantum dot: Atomic approach for the finite U-impurity Anderson model

We study the thermopower S, linear thermal conductance κ, linear electric conductance G and thermoelectric figure of merit Z properties of a single-walled zig–zag carbon nanotube side coupled to a correlated quantum dot (QD). We employ the recently developed U-finite atomic approach for the Single Impurity Anderson model (SIAM). The quantum dot is linked to the localized states in the model, considering a finite Coulombic repulsion U, and the conduction band in the model is associated with the single walled zig–zag metallic carbon nanotube (n=3), and is described by a tight-binding approximation in order to obtain Green׳s function of the nanotube. The thermoelectric transport coefficients were obtained using the Keldysh non-equilibrium Green׳s function technique with the Onsager relation in the linear regime automatically satisfied. Results indicate that this system can be employed in possible thermoelectric device applications at low temperatures when strong charge fluctuations are present in the QD.

Spin pumping and spin-transfer torques in antiferromagnets.

Spin pumping and spin-transfer torques are two reciprocal phenomena widely studied in ferromagnetic materials. However, pumping from antiferromagnets and its relation to current-induced torques have not been explored. By calculating how electrons scatter off a normal metal-antiferromagnetic interface, we derive pumped spin and staggered spin currents in terms of the staggered field, the magnetization, and their rates of change. For both compensated and uncompensated interfaces, spin pumping is of a similar magnitude as in ferromagnets with a direction controlled by the polarization of the driving microwave. The pumped currents are connected to current-induced torques via Onsager reciprocity relations.

Reciprocal relations in electroacoustics.

In a colloidal suspension, one can generate sound waves by the application of an alternating electric field (Electrokinetic Sonic Amplitude, i.e., ESA). Another phenomenon is electrophoresis (Electrophoretic Mobility, i.e., EM) where a colloidal particle moves relative to the solvent in an electric field. Vice versa one can generate electric fields or electric currents by sound waves (Colloid Vibration Potential/Current, i.e., CVP/CVI). In 1988 and 1990, O'Brien [J. Fluid Mech. 190, 71-86 (1988) and O'Brien, J. Fluid Mech. 212, 81-93 (1990)] derived a reciprocal relation between the proportionality coefficients of the EM and CVI phenomena. In this paper, we will generalize his proof by constructing the relevant entropy production from which the linear force-flux relations follow. General relations are derived for electrolyte solutions, of which colloidal suspensions are a particular case. The relations between CVI, CVP, EM, and ESA are discussed. O'Brien's reciprocal relation then follows as an Onsager relation. The relation is valid for any applied electric field frequency, particle surface charge and particle concentration (even in the presence of particle-particle interactions) provided the system is isotropic.

Anisotropic transport for parabolic, non-parabolic, and linear bands of different dimensions

We have developed a robust analytical methodology for modeling the anisotropic transport distribution function, which can be then used to describe various transport properties of anisotropic systems, including the electrical conductivity, carrier mobility, Seebeck coefficient, and thermal conductivity. Our methodology has considered the general cases for 3-, 2-, and 1-dimensional systems with parabolic, non-parabolic, and linear dispersion relations. Calculations are made using both the relaxation time approximation and the mean free path approximation. We have found that the Onsager relation can be violated under certain conditions. Furthermore, the methodology developed in the present work is compared with the traditionally used numerical methodology.

Crossed nonlocal effects and breakdown of the Onsager symmetry relation in a thermodynamic description of thermoelectricity

Nonlocal nonlinear effects coupling the heat flux and the electric-current density in an enlarged thermodynamic description of thermoelectric systems are considered. The influence of such terms on the breakdown of the Onsager reciprocity relation between the effective transport coefficients, depending on the electric field and the temperature gradient, is analyzed up to second-order in the thermodynamic forces. The maximum value of the thermoelectric efficiency is derived as a function of the figure-of-merit and of the degree of the Onsager symmetry breaking.

A theoretical study of biological membrane response to temperature gradients at the single-cell level

Recent experimental studies provide evidence for the existence of a spatially non-uniform temperature field in living cells and in particular in their plasma membrane. These findings have led to the development of a new and exciting field: thermal biology at the single-cell level. Here, we examine theoretically a specific aspect of this field, i.e. how temperature gradients at the single-cell level affect the phase behaviour and geometry of heterogeneous membranes. We address this issue by using the Onsager reciprocal relations combined with a simple model for a binary lipid mixture. We demonstrate that even small temperature variations along the membrane may introduce intriguing phenomena, such as phase separation above the critical temperature and unusual shape response. These results also suggest that the shape of a membrane can be manipulated by dynamically controlling the temperature field in its vicinity. The effects of intramembranous temperature gradients have never been studied experimentally. Thus, the predictions of the current contribution are of a somewhat speculative nature. Experimental verification of these results could mark the beginning of a new line of research in the field of biological membranes. We report our findings with the hope of inspiring others to perform such experiments.

Molecular dynamics simulation of electrokinetic flow of an aqueous electrolyte solution in nanochannels.

Electrokinetic flows of an aqueous NaCl solution in nanochannels with negatively charged surfaces are studied using molecular dynamics simulations. The four transport coefficients that characterize the response to weak electric and pressure fields, namely, the coefficients for the electrical current in response to the electric field (M(jj)) and the pressure field (M(jm)), and those for the mass flow in response to the same fields (M(mj) and M(mm)), are obtained in the linear regime using a Green-Kubo approach. Nonequilibrium simulations with explicit external fields are also carried out, and the current and mass flows are directly obtained. The two methods exhibit good agreement even for large external field strengths, and Onsager's reciprocal relation (M(jm) = M(mj)) is numerically confirmed in both approaches. The influence of the surface charge density on the flow is also considered. The values of the transport coefficients are found to be smaller for larger surface charge density, because the counter-ions strongly bound near the channel surface interfere with the charge and mass flows. A reversal of the streaming current and of the reciprocal electro-osmotic flow, with a change of sign of M(mj) due to the excess co-ions, takes places for very high surface charge density.

Pore network model of electrokinetic transport through charged porous media

We introduce a method for the numerical determination of the steady-state response of complex charged porous media to pressure, salt concentration, and electric potential gradients. The macroscopic fluxes of solvent, salt, and charge are computed within the framework of the Pore Network Model (PNM), which describes the pore structure of the samples as networks of pores connected to each other by channels. The PNM approach is used to capture the couplings between solvent and ionic flows which arise from the charge of the solid surfaces. For the microscopic transport coefficients on the channel scale, we take a simple analytical form obtained previously by solving the Poisson-Nernst-Planck and Stokes equations in a cylindrical channel. These transport coefficients are upscaled for a given network by imposing conservation laws for each pores, in the presence of macroscopic gradients across the sample. The complex pore structure of the material is captured by the distribution of channel diameters. We investigate the combined effects of this complex geometry, the surface charge, and the salt concentration on the macroscopic transport coefficients. The upscaled numerical model preserves the Onsager relations between the latter, as expected. The calculated macroscopic coefficients behave qualitatively as their microscopic counterparts, except for the permeability and the electro-osmotic coupling coefficient when the electrokinetic effects are strong. Quantitatively, the electrokinetic couplings increase the difference between the macroscopic coefficients and the corresponding ones for a single channel of average diameter.

Non-equilibrium Thermodynamic Extension of the Phenomenological Theories of First-order Phase Transitions

Because the phenomenological theories of phase transitions which are based on the equilibrium thermodynamics cannot describe the first-order phase transition processes accurately, the non-equilibrium thermodynamics was applied to extending the existing phenomenological theories of first-order phase transitions. First, the internal interactions of system at a first-order phase transition were considered. The nominal stress, the nominal volume force, the internal electric field and the internal magnetic field were introduced to characterize them. Then, the most general Gibbs equation except the factor of chemical reactions was established. Based on the conservation of energy and the transformation between internal energy and kinetic energy, the rate of local entropy production was deduced. Then based on the principle of minimum entropy production and the generalized Onsager reciprocal relations, the local, evolving characteristics of a first-order phase transition (e.g. a first-order ferroelectric phase transition) were described well. It makes up the inadequateness of the older phenomenological theories.

Non-equilibrium Thermodynamic Extension of the Phenomenological Theories of First-order Phase Transitions

Because the phenomenological theories of phase transitions which are based on the equilibrium thermodynamics cannot describe the first-order phase transition processes accurately, the non-equilibrium thermodynamics was applied to extending the existing phenomenological theories of first-order phase transitions. First, the internal interactions of system at a first-order phase transition were considered. The nominal stress, the nominal volume force, the internal electric field and the internal magnetic field were introduced to characterize them. Then, the most general Gibbs equation except the factor of chemical reactions was established. Based on the conservation of energy and the transformation between internal energy and kinetic energy, the rate of local entropy production was deduced. Then based on the principle of minimum entropy production and the generalized Onsager reciprocal relations, the local, evolving characteristics of a first-order phase transition (e.g. a first-order ferroelectric phase transition) were described well. It makes up the inadequateness of the older phenomenological theories.

Anisotropic magnetothermal transport and spin Seebeck effect

The anisotropic properties of thermal transport in insulating or conducting ferromagnets are derived on the basis of the Onsager reciprocity relations applied to a magnetic system. It is shown that the angular dependence of the temperature gradient takes the same form as that of the anisotropic magnetoresistance, including anomalous and planar Hall contributions. The measured thermocouple generated between the extremities of the nonmagnetic electrode in thermal contact to the ferromagnet follows this same angular dependence. The sign and amplitude of the magnetovoltaic signal is controlled by the difference of the Seebeck coefficients of the thermocouple.

Microwave response of a ballistic quantum dot

The microwave response (photovoltage and photoconductance) of a lateral ballistic quantum dot made of a high-mobility two-dimensional electron gas in an AlGaAs/GaAs heterojunction has been studied experimentally in the frequency range of 110–170 GHz. It has been found that the asymmetry of the photovoltage with respect to the sign of the magnetic field has mesoscopic character and depends on both the magnetic field and the microwave power. This indicates the violation of the Onsager reciprocity relations regarding the electron-electron interactions in the mesoscopic photovoltaic effect. A strong increase in the conductance of the quantum dot induced by the microwave radiation and unrelated to heating, as well as the microwave-induced magneto-oscillations, has been discovered.

Development of a Unifying Framework for Modeling Multi-component Diffusion in Polymer Solutions

In this work a unifying framework for modeling multi-component diffusion in mixed solvent polymer solutions is developed by introducing additional restrictions such as the Onsager reciprocal relations (ORR) and the quasi-equilibrium postulate. More specifically, three different multi-component diffusion models, namely the Zielinski and Hanley model, the Dabral et al. theory and the Alsoy–Duda model are revised by using the above restrictions which are based on sound principles of non-equilibrium thermodynamics. Realistic simulations for the solvent(s) evaporation from the water/acetone/cellulose acetate (CA) and formamide/acetone/CA systems were obtained by combining the above multi-component diffusion models with the ORR and the quasi-equilibrium postulate. It is believed that the results of this work could be used to further study diffusion in multi-component systems appearing in coating and membrane formation.

Transport with ultracold atoms at constant density

We investigate the transport through a few-level quantum system described by a Markovian master equation with temperature- and particle-density-dependent chemical potentials. From the corresponding Onsager relations we extract linear response transport coefficients in analogy to the electronic conductance, thermal conductance, and thermopower. Considering ideal Fermi and Bose gas reservoirs, we observe steady-state currents against the thermal bias as a result of the nonlinearities introduced by the constraint of a constant particle density in the reservoirs. Most importantly, we find signatures of the onset of Bose-Einstein condensation in the transport coefficients.

Multivariate fluctuation relations for currents

This paper is devoted to multivariate fluctuation relations for all the currents flowing across an open system in contact with several reservoirs at different temperatures and chemical potentials, or driven by time-independent external mechanical forces. After some transient behavior, the open system is supposed to reach a nonequilibrium steady state that is controlled by the thermodynamic and mechanical forces, called the affinities. The time-reversal symmetry of the underlying Hamiltonian dynamics implies symmetry relations among the statistical properties of the fluctuating currents, depending on the values of the affinities. These multivariate fluctuation relations are not only compatible with the second law of thermodynamics, but they also imply remarkable relations between the linear or nonlinear response coefficients and the cumulants of the fluctuating currents. These relations include the Onsager and Casimir reciprocity relations, as well as their generalizations beyond linear response. Methods to deduce multivariate fluctuation relations are presented for classical, stochastic and quantum systems. In this way, multivariate fluctuation relations are obtained for energy or particle transport in the effusion of an ideal gas, heat transport in Hamiltonian systems coupled by Langevin stochastic forces to heat reservoirs, driven Brownian motion of an electrically charged particle subjected to an external magnetic field, and quantum electron transport in multi-terminal mesoscopic circuits where the link to the scattering approach is established.

Energy transfer in a molecular motor in the Kramers regime

We present a theoretical treatment of energy transfer in a molecular motor described in terms of overdamped Brownian motion on a multidimensional tilted periodic potential. The tilt represents a thermodynamic force driving the system out of equilibrium and, for nonseparable potentials, energy transfer occurs between degrees of freedom. For deep potential wells, the continuous theory transforms to a discrete master equation that is tractable analytically. We use this master equation to derive formal expressions for the hopping rates, drift and diffusion, and the efficiency and rate of energy transfer in terms of the thermodynamic force. These results span both strong and weak coupling between degrees of freedom, describe the near and far from equilibrium regimes, and are consistent with generalized detailed balance and the Onsager relations. We thereby derive a number of diverse results for molecular motors within a single theoretical framework.

Investigation of Fickian diffusion in the ternary mixture of 1,2,3,4-tetrahydronaphthalene, isobutylbenzene, and dodecane

We present a comprehensive analysis of experimental results obtained for Fickian diffusion in the benchmark ternary liquid mixture of 1,2,3,4-tetrahydronaphthalene, isobutylbenzene, and dodecane (nC12) with equal mass fractions. Isothermal diffusion coefficients have been measured by two independent experimental methods: by Taylor dispersion technique, and by a counter flow cell fitted with an optical interferometry device. The experimental diffusion matrices have been critically analyzed regarding the Onsager reciprocal relations, for which we introduce a matrix asymmetry index s(2) that is independent of the frame of reference and the component order.

Entropic Fluctuations of Quantum Dynamical Semigroups

We study a class of finite dimensional quantum dynamical semigroups exp(tL) whose generators L are sums of Lindbladians satisfying the detailed balance condition. Such semigroup arise in the weak coupling (van Hove) limit of Hamiltonian dynamical systems describing open quantum systems out of equilibrium. We prove a general entropic fluctuation theorem for this class of semigroups by relating the cumulant generating function of entropy transport to the spectrum of a family of deformations of the generator L. We show that, besides the celebrated Evans-Searles symmetry, this cumulant generating function also satisfies the translation symmetry recently discovered by Andrieux et al., and that in the linear regime near equilibrium these two symmetries yield Kubo's and Onsager's linear response relations.