Onsager Relations Research Articles

Transport of ions in hydrophobic nanotubes

The theory of electrokinetic ion transport in cylindrical channels of a fixed surface charge density is revisited. Attention is focused on the impact of the hydrophobic slippage and mobility of adsorbed surface charges. We formulate generalized Onsager relations for a cylinder of an arbitrary radius and then derive exact expressions for the mean electro-osmotic mobility and conductivity. To employ these expressions, we perform additional electrostatic calculations with a special focus on the non-linear electrostatic effects. Our theory provides a simple explanation of a giant enhancement of the electrokinetic mobility and conductivity of hydrophobic nanotubes by highlighting the role of appropriate electrostatic and hydrodynamic length scales and their ratios. We also propose a novel interpretation of zeta potentials of cylindrical channels.

Numerical Test of the Onsager Relations in a Driven System.

The Onsager reciprocity relations were formulated in the context of irreversible thermodynamics, but they are based on assumptions that have a wider applicability. Here, we present simulations testing the Onsager relations between surface-coupled diffusive and bulk fluxes in a system prepared in a nonequilibrium steady state. The system consists of a mixture of two identical species maintained at different temperatures inside a channel. In order to tune the friction of the two species with the walls independently, while keeping the particle-wall interaction potentials the same, we allow the kinematics of particle-wall collisions to be different: "bounce-back" (B) or "specular" (S). In the BB case, diffusio-capillary transport can only take place if the two species have different temperatures. We find that the Onsager reciprocity relations are obeyed in the linear regime, even in the BB case where all fluxes are the result of perturbing the system from a nonequilibrium steady state in a way that does not satisfy time-reversal symmetry. Our Letter provides a direct, numerical illustration of the validity of the Onsager relations outside their original range of application, and suggests their relevance for transport in driven or active systems.

On the Validity of a Linearity Axiom in Diffusion and Heat Transfer

In this work, the linearity axiom of irreversible thermodynamics for diffusion and heat transfer has been re-examined. It is shown that this axiom is compatible with the entropy production invariance principle with respect to a reference quantity for diffusion and heat transfer in the Euclidean space. Moreover, the underlying relations of the other principles of irreversible thermodynamics for multi-component diffusion and heat transfer, such as the quasi-equilibrium and the Onsager reciprocal relations (ORR) with the entropy production invariance, are re-examined. It was shown that the linearity principle postulates for diffusion and heat transfer and could be directly derived from the entropy production invariance axiom. It is believed that this work could not only be used for the drying of polymer coatings but also for pedagogical purposes. It may also be generalized; thus, leading to a generalized framework for irreversible thermodynamics.

Onsager reciprocal relations and chemo-mechanical coupling for chemically active colloids.

Similar to cells, bacteria, and other micro-organisms, synthetic chemically active colloids can harness the energy from their environment through a surface chemical reaction and use the energy to self-propel in fluidic environments. In this paper, we study the chemo-mechanical coupling that leads to the self-propulsion of chemically active colloids. The coupling between chemical reactions and momentum transport is a consequence of Onsager reciprocal relations. They state that the velocity and the surface reaction rate are related to mechanical and chemical affinities through a symmetric matrix. A consequence of Onsager reciprocal relations is that if a chemical reaction drives the motion of the colloid, then an external force generates a reaction rate. Here, we investigate Onsager reciprocal relations for a spherical active colloid that catalyzes a reversible surface chemical reaction between two species. We solve the relevant transport equations using a perturbation expansion and numerical simulations to demonstrate the validity of reciprocal relations around the equilibrium. Our results are consistent with previous studies and highlight the key role of solute advection in preserving the symmetry of the Onsager matrix. Finally, we show that Onsager reciprocal relations break down around a nonequilibrium steady state, which has implications for the thermal fluctuations of the active colloids used in experiments.

Magnons in antiferromagnetic bcc Cr andCr2O3from time-dependent density functional theory

We apply time-dependent density functional theory to calculate the transverse magnetic susceptibility of bcc Cr and ${\mathrm{Cr}}_{2}{\mathrm{O}}_{3}$, which constitute prototypical examples of antiferromagnets with itinerant and localized magnetic moments, respectively. The exchange-correlation kernel is rescaled in order to enforce the Goldstone condition and the magnon dispersion relations are extracted based on a symmetry analysis relying on the generalized Onsager relation. Doing so, our calculations yield the characteristic linear magnon dispersion of antiferromagnets in the long-wavelength limit. In the case of ${\mathrm{Cr}}_{2}{\mathrm{O}}_{3}$, we find that the adiabatic local density approximation yields a good qualitative agreement with the measured dispersion, but overestimates the magnon velocity and bandwidth by a factor of 2. Including a Hubbard correction improves the magnon velocity, but at the expense of the overall qualitative agreement with the experimental magnon dispersion. For bcc Cr we find a sharp acoustic magnon mode at low energies with a velocity in agreement with previously reported values. At higher energies, the acoustic magnon mode becomes subject to strong Landau damping and rapidly vanishes once it enters the Stoner continuum. In addition to the acoustic magnon mode, we also observe an additional collective mode along the $\mathrm{\ensuremath{\Gamma}}\ensuremath{\rightarrow}\mathrm{R}$ direction with an energy of $\ensuremath{\sim}1$ eV, which is located inside the Stoner continuum, but appears to elude the effect of Landau damping.

Full counting statistics and fluctuation theorem for the currents in the discrete model of Feynman's ratchet.

We provide a detailed investigation of the fluctuations of the currents in the discrete model of Feynman's ratchet proposed by Jarzynski and Mazonka in 1999. Two macroscopic currents are identified, with the corresponding affinities determined using Schnakenberg's graph analysis. We also investigate full counting statistics of the two currents and show that fluctuation theorem holds for their joint probability distribution. Moreover, fluctuation-dissipation relation, Onsager reciprocal relation and their nonlinear generalizations are numerically shown to be satisfied in this model.

Aharonov-Bohm oscillations in the Majorana fermion modulated charge and heat transports through a double-quantum-dot interferometer

The Aharonov-Bohm (AB) oscillation effects of electric and heat currents through a parallel double-quantum-dot (DQD) interferometer coupled with Majorana bound states (MBSs) have been investigated. Local and nonlocal Andreev reflections make efficient contributions to the transports, and the AB oscillation structures are modified by the coupled MBSs explicitly. Four linear electric and thermal conductance components are generated by electric potential and temperature differences. The Onsager relation is invalid due to the presence of Andreev reflections in linear response region. However, when the coupling of MBSs is removed, the Andreev reflections disappear, and the Onsager relation is recovered. The magnitudes of electric and thermal conductances are enhanced due to coupling MBSs, and the overall oscillation period changes from flux quantum Φ0 to 2Φ0. We obtain quite different oscillation structures of Seebeck coefficient for the equal-level and unequal-level DQD systems, where peak-valley and higher-lower double-peak structures appear. Meanwhile, the magnitude of Seebeck coefficient is enlarged obviously due to applying MBSs. The AB oscillation behaviors of these coefficients provide novel signatures for detecting Majorana fermions by employing DQD interferometer.

Two-point functions from chiral kinetic theory in magnetized plasma

We study the two-point functions from chiral kinetic theory which characterize the response to perturbative vector and axial gauge fields in magnetized chiral plasma. In the lowest Landau level approximation, the solution of chiral kinetic equations gives density waves of electric and axial charges, which contain chiral magnetic wave implied by the axial anomaly and magnetic field. We then obtain the constitutive relations for covariant currents and stress tensor that involving the density waves. By considering the difference between consistent and covariant anomalies explicitly, the correlators of consistent currents and stress tensor satisfy derivative symmetry, and therefore allow an effective action for the perturbative gauge fields as the generating functional of the correlators. We also verify the derivative symmetry of the correlators agrees with the Onsager relations.

The Onsager Reciprocity Relations Revisited

The Onsager relations are discussed and it is suggested that they should be interpreted as there is a frame of reference where all the transport processes are independent. The concepts are illustrated with isobarothermal diffusion in simple metallic phases as well as complex ionic systems. A transformation from lattice-fixed frame of reference to number-fixed frame gives the Kirkendall effect as a cross effect.

Time reversal symmetry for classical, non-relativistic quantum and spin systems in presence of magnetic fields

We extend to quantum mechanical systems results previously obtained for classical mechanical systems, concerning time reversibility in presence of a magnetic field. As in the classical case, results like the Onsager reciprocal relations and the so-called fluctuation theorems, are consequently obtained, without recourse to the Casimir modification. The quantum systems treated here are non-relativistic, and are described by the Schrödinger equation or the Pauli equation. In particular, we prove that the spin-field interaction does not break the time reversal invariance (TRI) of the dynamics, and that it does not require additional conditions for such a symmetry to hold, compared to the spinless cases. These results are relevant for experiments such as diffusion in solutions, thermoelectricity and spin charge transport. Indeed, no violation of the Onsager relations has been found in presence of a magnetic field, contrary to general expectations.

Universal bounds on cooling power and cooling efficiency for autonomous absorption refrigerators.

For steady-state autonomous absorption refrigerators operating in the linear response regime, we show that there exists a hierarchy between the relative fluctuation of currents for cold, hot, and work terminals. Our proof requires the Onsager reciprocity relation along with the refrigeration condition that sets the direction of the mean currents for each terminal. As a consequence, the universal bounds on the mean cooling power, obtained following the thermodynamic uncertainty relations, follow a hierarchy. Interestingly, within this hierarchy, the tightest bound is given in terms of the work current fluctuation. Furthermore, the relative uncertainty hierarchy introduces a bound on cooling efficiency that is tighter than the bound obtained from the thermodynamic uncertainty relations. Interestingly, all of these bounds saturate in the tight-coupling limit. We test the validity of our results for two paradigmatic absorption refrigerator models: (i) a four-level working fluid and (ii) a two-level working fluid, operating in the weak (additive) and strong (multiplicative) system-bath interaction regimes, respectively.

On the Validity of Onsager Reciprocal Relations (ORR) for Heat Transfer in Anisotropic Solids

In this work, we investigate the validity of axioms such as Onsager Reciprocal Relations (ORR) for heat transfer in irreversible thermodynamics close to equilibrium. We show that the ORR for this case could be directly derived by introducing the widely accepted concept of heat transfer coefficients into the entropy production rate and by assuming that the thermal conductivity coefficients are uniquely defined. It is believed that this work can not only be used for pedagogical purposes but may also be generalized to other processes beyond heat transfer, thus leading to a generalized framework for transport phenomena and irreversible thermodynamics.

Time-reversal symmetry breaking and emergence in driven-dissipative Ising models

Fluctuation-dissipation relations (FDRs) and time-reversal symmetry (TRS), two pillars of statistical mechanics, are both broken in generic driven-dissipative systems. These systems rather lead to non-equilibrium steady states far from thermal equilibrium. Driven-dissipative Ising-type models, however, are widely believed to exhibit effective thermal critical behavior near their phase transitions. Contrary to this picture, we show that both the FDR and TRS are broken even macroscopically at, or near, criticality. This is shown by inspecting different observables, both even and odd operators under time-reversal transformation, that overlap with the order parameter. Remarkably, however, a modified form of the FDR as well as TRS still holds, but with drastic consequences for the correlation and response functions as well as the Onsager reciprocity relations. Finally, we find that, at criticality, TRS remains broken even in the weakly-dissipative limit.

Nonequilibrium Black Hole Thermodynamics in Anti-de Sitter Spacetime

This work discusses the black hole thermodynamics in a weak dynamical Anti-de Sitter spacetime, which should be described by the nonequilibrium thermodynamics, because the metric depends on the time coordinate. Taking the Vaidya-Anti-de Sitter black hole spacetime as an example, the local entropy balance equations and principle of minimum entropy generation are derived, and finally, some irreversible effects in nonequilibrium thermodynamics are studied by using the Onsager reciprocal relation.

Observations on the fourth-power scaling of high-pressure shock waves in solids

This paper is concerned with the bounds and approximations that are found in the original derivation of the fourth-power scaling of shock waves in solids [D. Grady, Appl. Phys. Lett. 38, 825 (1981)]. The analysis is focused on the framework of the derivation and is independent of constitutive assumption, such as visco-plastic behavior. Results include an upper bound for the shock pressure and a restriction on the range of power coefficient for materials having a power-type function for the shock velocity–particle velocity relation. Relaxation of this restriction is proposed based on the idea that the rise time along the Rayleigh line is strain dependent. The idea led to the application of the Onsager relation to strain rate calculation that in turn resulted in a quadratic function for the strain rate–shock pressure relation. The fourth-power relation is obtained by generalizing the Onsager relation through the introduction of a quadratic dissipative potential in analogy to Rayleigh's dissipative potential.

Fluctuation theorem for spin transport at insulating ferromagnetic junctions

General relations for nonequilibrium spin transport at a magnetic junction between a normal metal and a ferromagnetic insulator are derived from the quantum fluctuation theorem. They include the extended Onsager relations between the spin conductance and the spin-current noise that hold for nonequilibrium states driven by an external current. These relations are valid for a general setup of spin Hall magnetoresistance (SMR) when the main contribution is due to the interfacial spin conductance. Unidirectional spin Hall magnetoresistance (UMR) in insulating ferromagnetic junctions can be understood in a similar way. Therefore, our work can provide a comprehensive viewpoint for understanding of SMR and UMR in insulating ferromagnetic junctions. Our result also predicts relations for higher-order coefficients with respect to the external current in terms of higher-order cumulants in a unified framework.

Separation of motions and vibrational separation of fractions for biocide brass

The mathematical method of separation of motions represents the effect of fast high-frequency oscillations by an effective averaged force or potential. Ultrasound acoustic vibrations are an example of such rapid oscillations leading to cavitation in water due to the gas phase formation (bubbles). Ultrasound cavitation is used to treat the surface of brass microparticles submerged in water. The formation of bubbles and their collapse triggers the modification of surface roughness and chemical composition. Consequently, the suspension separates into various fractions related to demonstrating biocide properties. While the exact mechanism of this process is complex, it can be explained phenomenologically by using the Onsager reciprocal relations for coupling the copper ion diffusion with the gas phase separation in water as a result of the action of the effective average vibrational force.

ДИНАМИКА ГАЗОВЫДЕЛЕНИЯ С ПОВЕРХНОСТИ ОБНАЖЕНИЯ ГАЗОНОСНЫХ УГОЛЬНЫХ ПЛАСТОВ СРЕДНЕЙ МОЩНОСТИ

The goal of the research was to clarify the regularities of the dynamics of gas release from the surface of the outcrop of the developed coal seam. The main research methods were theoretical methods of mathematical physics and non-equilibrium thermodynamics. Gas-bearing coal seams are usually mined underground. When driving development workings, outcropping surfaces of gas-bearing coal seams appear and gases in the seams under excessive pressure are released into the atmosphere of the mine workings. Gas-bearing coal seams are usually mined underground. When driving preparatory workings, surfaces of outcropping of gas-bearing coal seams arise and gases that are in the seams under excessive pressure are released into the atmosphere of the mine workings. The most important gas-dynamic characteristic of this process is the rate of gas release, which represents the volume of gases released from a unit area of exposure of a coal seam per unit of time. A generalized law of resistance for gas filtration in a rock mass is recommended, and a fairly rigorous thermodynamic substantiation is given. It is shown that the densities of gas mass flows in accordance with the postulate of their linear relationship with the driving forces are determined by the Onsager relation. The results obtained and their discussion is presented. Mathematical models are proposed for engineering calculations of the dynamics of methane release from the outcropping surface of medium-thick coal seams. The error of the adopted approximations does not exceed 3%. The intensity of methane release is directly related to the planogram of work in the working face. Analysis of this dependence indicates that during the extraction cycle, methane release increases due to an increase in the area of the gas-release surface. The main conclusions are as follows: mathematical modeling of the processes of gas movement in a porous sorbing medium using approximate mathematical models representing linearized equations of mathematical physics; the regularities of the dynamics of the rate of gas release from the surface of the outcrop of a gas-bearing coal seam is the theoretical basis for the mathematical description of the process of gas release; the use of a linearized hyperbolic filtration equation most accurately describes the processes of methane release from the outcropping surface of mined coal seams.

Non-reciprocal magnetoresistance, directional inhomogeneity and mixed symmetry Hall devices

Phenomenology similar to the non-reciprocal charge transport violating Onsager's reciprocity relations can develop in directionally inhomogeneous conducting films with non-uniform Hall coefficient along the current trajectory. The effect is demonstrated in ferromagnetic CoPd films and analyzed in comparison with the unidirectional magnetoresistance phenomena. We suggest to use an engineered inhomogeneity for spintronics applications and present the concept of mixed symmetry Hall devices in which transverse to current Hall signal is measured in a longitudinal contacts arrangement. Magnetization reversal and memory detection are demonstrated in the three-terminal and the partitioned normal metal–ferromagnet (NM-FM) device designs. Multi-bit memory is realized in the partitioned FM-NM-FM structure. The relative amplitude of the antisymmetric signal in the engineered ferromagnetic devices is few percent, which is 10–103 times higher than in their unidirectional magnetoresistance analogues.

Flux dependent current rectification in geometrically symmetric interconnected triple-dot Aharanov-Bohm interferometer

We propose and investigate a nonreciprocal performance of a triple-dot Aharonov-Bohm interferometer in the non-linear regime. We study the steady-state behavior of the nonequilibrium triple-dot Aharonov-Bohm (AB) interferometer using analytical tools and numerical simulations. Our simple setup includes noninteracting three quantum dots placed on the vertex of an equilateral triangle. Out of these three dots, two dots are coupled to two biased metallic leads at the same strength and the third one is connected with a probe that can mimics the elastic and inelastic scattering mechanisms. A magnetic flux Φ pierces the interferometer perpendicularly. We observe a magnetic-flux dependent current rectification induced by inelastic scattering by voltage probe in the nonlinear regime, but this rectification is absent in the linear regime. Our investigation reveals that the rectification for our 3-dots AB set up maximize when the inter-dot tunneling strength, t , matches with the hybridization strength, γ , between a dot and metallic lead. Downright, we can say that our study furnishes the working principles and rectification efficiency of a triple-dot AB interferometer. One can use this simple setup to design a nano-scale rectifier . • We demonstrate broken Onsager reciprocity relation in a triple dot Aharanov-Bohm interferometer model. • This exactly solvable model can unravel the interplay of quantum coherence and environmental decoherence effect.