Onsager Relations Research Articles

BRAID GROUP ACTION AND ROOT VECTORS FOR THE q-ONSAGER ALGEBRA

We define two algebra automorphisms Ͳ0 and Ͳ1 of the q-Onsager algebra {mathcal{B}}_c , which provide an analog of G. Lusztig's braid group action for quantum groups. These automorphisms are used to define root vectors which give rise to a PBW basis for {mathcal{B}}_c . We show that the root vectors satisfy q-analogs of Onsager's original commutation relations. The paper is much inspired by I. Damiani's construction and investigation of root vectors for the quantized enveloping algebra of hat{mathfrak{s}{mathfrak{l}}_2} .

Atomic-scale modeling of the thermodynamic and kinetic properties of dilute alloys driven by forced atomic relocations

Sustained external forces acting on a material provide additional mechanisms to evolve the state of the system, and these mechanisms do not necessarily obey the microscopic detailed balance. Therefore, standard methods to compute the thermodynamic and kinetic properties do not apply in such driven systems. The competition between these mechanisms and the standard thermally activated jumps leads to non-equilibrium steady states. We extend the Self-Consistent Mean Field theory to take into account forced atomic relocations (FARs) as a model of these additional kinetic mechanisms. The theory is applied to the atomic-scale modelling of radiation damage. Using a first-shell approximation of the theory, we highlight the violation of Onsager reciprocal relations in driven systems. An implementation of the extended theory into the KineCluE code yields calculations of the effective Onsager coefficients in agreement with Monte Carlo simulations. A systematic parametric study is performed to emphasize the effect of FAR distances and the solute-defect interaction on the diffusion properties. The effect of FAR on the vacancy-solute flux coupling and the solute tracer diffusivity is non-negligible when: (i) the solute-vacancy thermodynamic attraction is large, (ii) the magnitude of the thermal jump frequencies is lower or comparable to the frequencies of FAR, and (iii) the range of interactions between vacancies and solute atoms is close to FAR distances.

Survival of the Quantum Anomalous Hall Effect in Orbital Magnetic Fields as a Consequence of the Parity Anomaly.

Recent experimental progress in condensed matter physics enables the observation of signatures of the parity anomaly in two-dimensional Dirac-like materials. Using effective field theories and analyzing band structures in external out-of-plane magnetic fields (orbital fields), we show that topological properties of quantum anomalous Hall (QAH) insulators are related to the parity anomaly. We demonstrate that the QAH phase survives in orbital fields, violates the Onsager relation, and can be therefore distinguished from a quantum Hall (QH) phase. As a fingerprint of the QAH phase in increasing orbital fields, we predict a transition from a quantized Hall plateau with σ_{xy}=-e^{2}/h to a not perfectly quantized plateau, caused by scattering processes between counterpropagating QH and QAH edge states. This transition can be especially important in paramagnetic QAH insulators, such as (Hg,Mn)Te/CdTe quantum wells, in which exchange interaction and orbital fields compete.

Are Onsager's reciprocal relations necessary to apply Thermodynamic Extremal Principles?

Onsager's Reciprocal Relations between thermodynamic forces and fluxes, for which Onsager was awarded the Nobel Prize, automatically follow from Thermodynamic Extremal Principles. Thus, the Principles are up to now non-applicable for the treatment of experimentally determined or theoretically modeled non-reciprocal systems as e.g. those in the magnetic field. However, we can demonstrate that adding of a certain barrier constraint as bilinear form of thermodynamic forces and fluxes accounted by the Thermodynamic Extremal Principles provides to non-reciprocal relations between the thermodynamic forces and fluxes. Such a novel idea may contribute to a better understanding of physics behind non-reciprocal systems.

A simple statistical-mechanical interpretation of Onsager reciprocal relations and Derjaguin theory of thermo-osmosis.

The application of a temperature gradient along a fluid-solid interface generates stresses in the fluid causing "thermo-osmotic" flow. Much of the understanding of this phenomenon is based on Derjaguin's work relating thermo-osmotic flows to the mechano-caloric effect, namely, the interfacial heat flow induced by a pressure gradient. This is done by using Onsager's reciprocity relationship for the equivalence of the thermo-osmotic and mechano-caloric cross-term transport coefficients. Both Derjaguin theory and Onsager framework for out-of-equilibrium systems are formulated in macroscopic thermodynamics terms and lack a clear interpretation at the molecular level. Here, we use statistical-mechanical tools to derive expressions for the transport cross-coefficients and, thereby, to directly demonstrate their equality. This is done for two basic models: i) an incopressible continuum solvent containing non-interacting solute particles, and ii) a single-component fluid without thermal expansivity. The derivation of the mechano-caloric coefficient appears to be remarkably simple, and provides a simple interpretation for the connection between interfacial heat and particle fluxes. We use this interpretation to consider yet another example, which is an electrolyte interacting with a uniformly charged surface in the strong screening (Debye-Hückel) regime.

Comparing theory and simulation for thermo-osmosis

We report a numerical study of thermo-osmotic slip, i.e., the particle flux induced by a thermal gradient along a solid-fluid interface. To facilitate comparison with theory, we consider a model of an ideal but viscous gas. We compare three numerical routes to obtain the slip coefficient: (1) by using the Onsager reciprocity relations, (2) by using the appropriate Green-Kubo relation, and (3) via the excess enthalpy. The numerical results are found to be mutually consistent and to agree with the theoretical prediction based on the assumption that hydrodynamics and thermodynamics are locally valid.

Theory of spin detection on the surface of diffusive topological insulators by means of ferromagnets: Establishing Onsager reciprocity and the importance of tunnel contact

A charge current on the surface of a topological insulator (TI) produces a surface spin polarization that can be measured experimentally using a ferromagnetic (FM) tunnel contact either in a three-terminal or a four-terminal potentiometric measurement. The potential measured on the FM contact depends on the direction and the magnitude of the surface charge current, as well as the FM magnetization direction relative to the spin polarization on the surface of the TI. In such a measurement, the resistance always obeys Onsager reciprocity, i.e., ${R}_{ab,cd}(+\stackrel{P\vec}{M})={R}_{cd,ab}(\ensuremath{-}\stackrel{P\vec}{M})$, where ${R}_{ab,cd}$ is the resistance measured with current injected between contacts $a$ and $b$, voltage measured between contacts $c$ and $d$, and the FM having magnetization $\stackrel{P\vec}{M}$. In a two-terminal measurement in which the current and the voltage contacts are the same, Onsager reciprocity dictates that the resistance remains the same even after the magnetization of the FM is reversed, i.e., ${R}_{ab,ab}(+\stackrel{P\vec}{M})={R}_{ab,ab}(\ensuremath{-}\stackrel{P\vec}{M})$. However, previous theories [Phys. Rev. Lett. 105, 066802 (2010), Europhys. Lett. 93, 67004 (2011)] claimed that change of resistance in such two-terminal measurement on the surface of a diffusive TI is possible upon reversing the FM magnetization direction. Here, we resolve this conflicting issue by showing that the Onsager reciprocity relation remains valid even in a two-terminal measurement on the surface of a diffusive TI. We consider the modifications in both the continuity equation of the charge density and the charge current density on the surface of the TI due to the effect of tunneling of electrons from the FM tunnel contact. We derive the transport equations on the surface of the TI from full quantum mechanical kinetic equation based on Keldysh Green's function, and obtain the resistance measured in a two-terminal or a multiterminal measurement after solving the transport equations analytically. We establish the validity of the Onsager reciprocity relation in both the two-terminal and the multiterminal measurements and also show the crucial importance of the tunnel contact in such spin detection experiments.

Interaction without back action in the context of quantum manipulation

We address the interaction between two quantum systems (A and B) that is mediated by their common linear environment. If the environment is out of equilibrium the resulting interaction violates Onsager relations and cannot be described by a Hamiltonian. In simple terms the action of system A on system B does not necessarily produce a back-action. We derive general quantum equations describing the situation and analyze in details their classical correspondence. Changing the properties of the environment one can easily change and engineer the resulting interaction. It is tempting to use this for quantum manipulation of the systems. However the resulting quantum gate is not always unitary and may induce a loss of quantum coherence. For a relevant example we consider systems A and B to be spins of arbitrary values and arrange the interaction to realize an analogue of the two-qubit CNOT gate. The direction of spin A controls the rotation of spin B while spin A is not rotated experiencing no back-action from spin B. We solve the quantum dynamics equations and analyze the purity of the resulting density matrix. The resulting purity essentially depends on the initial states of the systems. We attempt to find a universal characteristics of the purity optimizing it for the worst choice of initial states. For both spins $s_A=s_B=1/2$, the optimized purity is bounded by 1/2 irrespective of the details of the gate. We also study in detail the semiclassical limit of large spins. In this case the optimized purity is bounded by $(1+\pi/2)^{-1}\approx0.39$. This is much better than the typical purity of a large spin state $\sim s^{-1}$. We conclude that although the quantum manipulation without back-action inevitably causes decoherence of the quantum states the actual purity of the resulting state can be optimized and made relatively high.

Charge-current correlation equalities for quantum systems far from equilibrium

We prove that a recently derived correlation equality between conserved charges and their associated conserved currents for quantum systems far from equilibrium [O.A. Castro-Alvaredo, B. Doyon, and T. Yoshimura, Phys. Rev. X 6, 041065 (2016)], is valid under more general conditions than assumed so far. Similar correlation identities, which in generalized Gibbs ensembles give rise to a current symmetry somewhat reminiscent of the Onsager relations, turn out to hold also in the absence of translation invariance, for lattice models, and in any space dimension, and to imply a symmetry of the non-equilibrium linear response functions.

Electrokinetic energy conversion of two-layer fluids through nanofluidic channels

Based on the Onsager reciprocal relation in the linear response regime, we first clarify the equivalence of thermodynamic and electric circuit analyses for electrokinetic energy conversion. Then we present a streaming-potential-based nanofluidic energy conversion system which comprises two immiscible fluids that form a flat interface in a slit-like channel. The validity of the Onsager reciprocal relation to such a two-fluid system is verified. The performance of such an energy converter is illustrated by considering two concrete oil–water systems with different properties. In both cases, we predict that the binary system with a thin oil layer increases both the maximum output power and the energy conversion efficiency, and this enhancement depends strongly on the mobile charges present at the oil–water interface, the salt concentration and the interface location. Concretely, for negatively charged interfaces, we find that the optimal efficiency increases with the interfacial charge for relatively thin oil layers; while for relatively thick oil layers, the interfacial charge has the opposite effect (i.e. reduction effect) on the energy conversion efficiency in the ranges of the parameters. We further investigate these systems from the viewpoint of energy transfer by deriving the related energy equation. We find that viscous dissipation consumes most of the power (more than 90 %), in both single-phase and two-fluid flows. However, the ratio of the viscous dissipation to the power input decreases with increase of the interfacial charge density for the case of a relatively thin oil layer in two-fluid flows. Meanwhile, although the presence of interfacial charges can lead to an increase in electrical dissipation, the amount of the increased power consumption is less than that of the reduced viscous dissipation in the case of a thin oil layer. Therefore, for two-fluid energy converters, the total power consumption can be reduced and the efficiency is improved.

Microreversibility, fluctuations, and nonlinear transport in transistors.

We present a stochastic approach for charge transport in transistors. In this approach, the electron and hole densities are governed by diffusion-reaction stochastic differential equations satisfying local detailed balance and the electric field is determined with the Poisson equation. The approach is consistent with the laws of electricity, thermodynamics, and microreversibility. In this way, the signal amplifying effect of transistors is verified under their working conditions. We also perform the full counting statistics of the two electric currents coupled together in transistors and we show that the fluctuation theorem holds for their joint probability distribution.Similarresults are obtained including the displacement currents. In addition, the Onsager reciprocal relations and their generalizations to nonlinear transport properties deduced from the fluctuation theorem are numerically shown to be satisfied.

Breakdown of the Sharvin limit in spin pumping with interfacial Rashba spin-orbit coupling

We theoretically investigate the role of the interfacial Rashba spin-orbit coupling in spin pumping based on a nonperturbative calculation. A nonmonotonic behavior is predicted in the Rashba-strength dependence of the Gilbert damping coefficients. We show that the in-plane damping component can exceed the Sharvin limit thanks to the Rashba-field-induced torque. Nevertheless, the pumped spin current remains below the Sharvin limit and satisfies the Onsager reciprocity relations with the spin-current-induced spin-transfer torque.

Determining phoretic mobilities with Onsager's reciprocal relations: Electro- and thermophoresis revisited.

We use a hydrodynamic reciprocal approach to phoretic motion to derive general expressions for the electrophoretic and thermophoretic mobility of weakly charged colloids in aqueous electrolyte solutions. Our approach shows that phoretic motion can be understood in terms of the interfacial transport of thermodynamic excess quantities that arises when a colloid is kept stationary inside a bulk fluid flow. The obtained expressions for the mobilities are extensions of previously known results as they can account for different hydrodynamic boundary conditions at the colloidal surface, irrespective of how the colloid-fluid interaction range compares to the colloidal radius.

To the substantiation in the framework of nonextensive Tsallis statistics of Onsager's reciprocity relations for kinetic coefficients

To the substantiation in the framework of nonextensive Tsallis statistics of Onsager's reciprocity relations for kinetic coefficients

Steepest-entropy-ascent model of mesoscopic quantum systems far from equilibrium along with generalized thermodynamic definitions of measurement and reservoir

This paper presents a nonequilibrium, first-principles, thermodynamic-ensemble based model for the relaxation process of interacting non-equilibrium systems. This model is formulated using steepest-entropy-ascent quantum thermodynamics (SEAQT) and its equation of motion for a grand canonical ensemble and is applied to a many particle system of classical or indistinguishable particles. Two kinds of interactions are discussed, including pure heat diffusion and heat and mass diffusion together. Since no local equilibrium assumption is made, the conjugate fluxes and forces are intrinsic to the subspaces of the state space of one system and/or of the state space of the two interacting systems. They are derived via the concepts of hypoequilibrium state and nonequilibrium intensive properties, which describe the nonmutual equilibrium status between subspaces of the thermodynamic state space of a single system and/or of the state space of the two interacting systems. The Onsager relations are shown to be thermodynamic kinematic features of the system and are found without knowledge of the detailed mechanics of the dynamic process. A fundamental thermodynamic explanation for the measurement of each intensive property of a system in a nonequilibrium state is given. The fundamental thermodynamic definition of reservoir is also discussed. Finally, the equation of motion for a system undergoing multiple interactions is provided, which permits the modeling of a network of local systems in nonequilibrium at any spatial and temporal scale.

Magnonic noise and Wiedemann-Franz law

We theoretically establish mutual relations among magnetic momentum, heat, and fluctuations of propagating magnons in a ferromagnetic insulating junction in terms of noise and the bosonic Wiedemann-Franz (WF) law. Using the Schwinger-Keldysh formalism, we calculate all transport coefficients of a noise spectrum for both magnonic spin and heat currents, and establish Onsager relations between the thermomagnetic currents and the zero-frequency noise. Making use of the magnonic WF law and the Seebeck coefficient in the low-temperature limit, we theoretically discover universal relations, i.e. being independent of material parameters, for both the nonequilibrium and equilibrium noise, and show that each noise is described solely in terms of thermal conductance. Finally, we introduce a magnonic spin-analog of the Fano factor, noise-to-current ratio, and demonstrate that the magnonic spin-Fano factor reduces to a universal value in the low-temperature limit and it remains valid even beyond a linear response regime.

Evaporation Boundary Conditions for the Linear R13 Equations Based on the Onsager Theory.

Due to the failure of the continuum hypothesis for higher Knudsen numbers, rarefied gases and microflows of gases are particularly difficult to model. Macroscopic transport equations compete with particle methods, such as the Direct Simulation Monte Carlo method (DSMC), to find accurate solutions in the rarefied gas regime. Due to growing interest in micro flow applications, such as micro fuel cells, it is important to model and understand evaporation in this flow regime. Here, evaporation boundary conditions for the R13 equations, which are macroscopic transport equations with applicability in the rarefied gas regime, are derived. The new equations utilize Onsager relations, linear relations between thermodynamic fluxes and forces, with constant coefficients, that need to be determined. For this, the boundary conditions are fitted to DSMC data and compared to other R13 boundary conditions from kinetic theory and Navier–Stokes–Fourier (NSF) solutions for two one-dimensional steady-state problems. Overall, the suggested fittings of the new phenomenological boundary conditions show better agreement with DSMC than the alternative kinetic theory evaporation boundary conditions for R13. Furthermore, the new evaporation boundary conditions for R13 are implemented in a code for the numerical solution of complex, two-dimensional geometries and compared to NSF solutions. Different flow patterns between R13 and NSF for higher Knudsen numbers are observed.

Conserved spin current for the Mott relation

The conserved bulk spin current [Shi et al., Phys. Rev. Lett. 96, 076604 (2006)], defined as the time derivative of the spin displacement operator, ensures automatically the Onsager relation between the spin Hall effect (SHE) and the inverse SHE. Here, we reveal another desirable property of this conserved spin current: the Mott relation linking the SHE and its thermal counterpart, the spin Nernst effect (SNE). According to the Mott relation, the SNE is known once the SHE is understood. In a two-dimensional Dirac-Rashba system with a smooth scalar disorder potential, we find a sign change of the spin Nernst conductivity when tuning the chemical potential.

Onsager reciprocity relation for ballistic phonon heat transport in anisotropic thin films of arbitrary orientation

Onsager reciprocity relation for ballistic phonon heat transport in anisotropic thin films of arbitrary orientation

The relationship between phase composition and conditions of sintering seawater derived magnesium oxide

This study has focused on the favourable effect of the TiO2 addition (1, 2 and 5 wt%) on the reduction of B2O3 content during activated sintering of magnesium oxide from seawater at temperatures of 1400, 1500 and 1700°C for the duration of 1, 2 and 4 h. A mathematical model of dependence between the B2O3 mass fraction in the sintered sample, the temperature of isothermal sintering, the isothermal sintering time and the mass fraction of TiO2 added have been proposed. Magnesium oxide was obtained from seawater by substoichiometric precipitation, with the addition of 80% of dolomite lime as the precipitation agent. New phases formed in magnesium oxide samples were examined by the XRD and SEM/EDS analysis. The results indicate that during activated sintering of seawater-derived magnesium oxide with a TiO2 addition, reactions of formation of Ca2B2O5, CaTiO3 and Mg2TiO4 took place simultaneously. The thermodynamics analysis of experimental results, based on the Onsager reciprocity relations (symmetry relations), was applied and phenomenological coefficients were calculated to describe the interference of these three irreversible processes.