Onsager Relations Research Articles

A thermodynamic based constitutive model considering the mutual influence of multiple physical fields

In multiple physical fields, the mutual influence among these fields can significantly impact material elastoplasticity. This paper proposes a thermodynamic-based constitutive model that incorporates the mutual influence of multiple physical fields. Rather than treating physical field characteristics as adjustable “parameters” affecting material coefficients, the proposed model employs a thermodynamic dissipation potential derived from the Onsager reciprocity relations, accounting for thermodynamic forces coupling. This dissipation potential ensures that the thermodynamic flow in the stress field is influenced by both stress field and other physical fields thermodynamic forces, which describes the plastic flow under multiple physical fields, while preserving thermodynamic duality. The paper begins with the formulation of a generalized thermodynamic model applicable to diverse materials and types of coupled fields, which is then degraded to a specific model for AA5182-O AlMg alloy under the influence of temperature and strain rate fields coupling. Given the universal applicability of the generalized model, such degradation provides a structured approach framework for developing thermodynamics-based constitutive models. For different materials encountered in practical engineering, new thermodynamic forces can be introduced to describe their unique mechanical properties while preserving the overarching thermodynamics-based model framework, thereby facilitating model scalability. The paper concludes with a validation example, showing that within the Portevin-Le Chatelie (PLC) regime, the plastic flow stress of AA5182-O AlMg alloy decreases with increasing strain rate at low temperatures but increases at high temperatures. The accurate simulation of these distinct strain rate effects crucially relies on integrating the mutual influence of temperature field and strain rate field.

Quantum Onsager relations

Abstract Using quantum information geometry, I derive quantum generalizations of the Onsager rate equations, which model the dynamics of an open system near a steady state. The generalized equations hold for a flexible definition of the forces as well as a large class of statistical divergence measures and quantum-Fisher-information metrics beyond the conventional definition of entropy production. I also derive quantum Onsager-Casimir relations for the transport tensors by proposing a general concept of time reversal and detailed balance for open quantum systems. The results establish a remarkable connection between statistical mechanics and parameter estimation theory.

Shubnikov–de Haas effect in the Falicov–Kimball model: strong correlation meets quantum oscillation

Abstract We present a comprehensive investigation of quantum oscillations (QOs) in the strongly-correlated Falicov-Kimball model (FKM). The FKM is a particularly suitable platform for probing the non-Fermi liquid state devoid of quasiparticles, affording exact Monte Carlo simulation across all parameter spaces.
In the high-correlation regime, we report the presence of prominent QOs in magnetoresistance and electron density at low temperatures within the phase separation state. The frequency behavior of these oscillations uncovers a transition in the Fermi surface as electron density diminishes, switching from hole-like to electron-like. Both types of Fermi surfaces are found to conform to the Onsager relation, establishing a connection between QOs frequency and Fermi surface area.
Upon exploring the temperature dependence of QOs amplitude, we discern a strong alignment with the Lifshitz-Kosevich (LK) theory, provided the effective mass is suitably renormalized. Notwithstanding, the substantial enhancement of the overall effective mass results in a notable suppression of the QOs amplitude within the examined temperature scope, a finding inconsistent with Fermi liquid predictions. For the most part, the effective mass diminishes as the temperature increases, but an unusual increase is observed at the proximity of the second-order phase transition instigated by thermal effects.
As the transition ensues, the regular QOs disappear, replaced by irregular ones in the non-Fermi liquid state under a high magnetic field.
We also uncover significant QOs in the insulating charge density wave state under weak interactions ($0 < U < 1$), a phenomenon we elucidate through analytical calculations.
Our findings shed light on the critical role of quasiparticles in the manifestation of QOs, enabling further understanding of their function in this context.

On the Elimination of Fast Variables from the Langevin Equation.

In a multivariable system, there are usually a number of relaxation times. When some of the relaxation times are shorter than others, the corresponding variables will decay to their equilibrium value faster than the others. After the fast variables have decayed, the system can be described with a smaller number of variables. From the theory of nonequilibrium thermodynamics, as formulated by Onsager, we know that the coefficients in the linear flux-force relations satisfy the so-called Onsager symmetry relations. The question we will address in this paper is how to eliminate the fast variables in such a way that the coefficients in the reduced description for the slow variables still satisfy the Onsager relations. As the proof that Onsager gave of the symmetry relations does not depend on the choice of the variables, it is equally valid for the subset of slow variables. Elimination procedures that lead to symmetry breaking are possible, but do not consider systems that satisfy the laws of nonequilibrium thermodynamics.

Multispecies Bhatnagar-Gross-Krook models and the Onsager reciprocal relations.

It is shown that most of the existing versions of the Bhatnagar-Gross-Krook model-those whose coefficient are independent of the molecular velocity-do not satisfy the Onsager relations. This circumstance poses a problem when calibrating these models, making their transport properties match those of a specific fluid.

Onsager relations between spin currents and charge currents

Onsager relations between spin currents and charge currents

Power efficiency of Hall-like devices: Comparison between reciprocal and antireciprocal Onsager relations

Power efficiency of Hall-like devices: Comparison between reciprocal and antireciprocal Onsager relations

Nonreciprocity and odd viscosity in chiral active fluids

Odd viscosity couples stress to strain rate in a dissipationless way. It has been studied in plasmas under magnetic fields, superfluid [Formula: see text], quantum-Hall fluids, and recently in the context of chiral active matter. In most of these studies, odd terms in the viscosity obey Onsager reciprocal relations. Although this is expected in equilibrium systems, it is not obvious that Onsager relations hold in active materials. By directly coarse-graining the kinetic energy and independently using both the Poisson-bracket formalism and a kinetic theory derivation, we find that the appearance of a nonvanishing angular momentum density, which is a hallmark of chiral active materials, necessarily breaks Onsager reciprocal relations. This leads to a non-Hermitian dynamical matrix for the total hydrodynamic momentum and to the appearance of odd viscosity and other nondissipative contributions to the viscosity. Furthermore, by accounting for both the angular momentum density and interactions that lead to odd viscosity, we find regions in the parameter space in which 3D odd mechanical waves propagate and regions in which they are mechanically unstable. The lines separating these regions are continuous lines of exceptional points, suggesting a possible nonreciprocal phase transition.

Numerical modeling and simulation of near-contact-line evaporation kinetics

A mathematical model of the liquid-vapor interface based on the Onsager reciprocity relations and the kinetic theory of gases is proposed. In the framework of this model, the heat and mass fluxes through an interface are related to the pressure and temperature jumps across it. The developed model is applied to the wedge-type geometry to simulate near-contact-line behaviors, where the kinetic effects are of paramount importance in view of flux singularities. The results of implementation of this model to the case of FC-72 evaporation are shown in comparison to a very widely used Schrage-type relation.

Heat and charge transport in interacting nanoconductors driven by time-modulated temperatures

We investigate the quantum transport of the heat and the charge through a quantum dot coupled to fermionic contacts under the influence of time modulation of temperatures. We derive, within the nonequilibrium Keldysh Green’s function formalism, generic formulas for the charge and heat currents by extending the concept of gravitational field introduced by Luttinger to the dynamically driven system and by identifying the correct form of dynamical contact energy. In linear response regime our formalism is validated from satisfying the Onsager reciprocity relations and demonstrates its utility to reveal nontrivial dynamical effects of the Coulomb interaction on charge and energy relaxations.

Analytical irreversible thermodynamics in conduction-radiative heat transfer of neutral gases through a lens of thermal radiation fields

An analytical investigation has been conducted on the steady-state conduction and a diluted gas exposed to a thermal radiation field experiences radiative heat transfer. Analytical solutions have been derived for the transport Boltzmann BGK partial differential equations system. The investigation delves into the irreversible thermodynamic behavior of the system through the utilization of the Liu-Lees model, which employs two-stream Maxwellian distribution functions. The moment approach is utilized to predict the behavior of macroscopic gas parameters like temperature, concentration, and Fourier heat flux. This process entails substituting these parameters into the two-stream Maxwellian distribution functions to analyze the system's non-equilibrium thermodynamic characteristics, which encompass gas particles and the heated plate. Through this analysis, kinetic coefficients, entropy, entropy flux, entropy production, and thermodynamic forces are determined. The investigation assesses the validation of Onsager's reciprocity relation, the Boltzmann H-theorem, the Le Chatelier principle, and the second law of thermodynamics within the system. Furthermore, the Gibbs formula is employed to estimate the ratios between various contributions to internal energy changes, which are determined by the total derivatives of extensive parameters. The non-equilibrium velocity distribution function was calculated for the first time, and its behavior was compared with that of the equilibrium one using 3D graphics. The behavior of the computed variables is predicted through graphical analysis and discussion of the results.

Anisotropic Klemens model for the thermal conductivity tensor and its size effect

With the constraint from Onsager reciprocity relations, here we generalize the Klemens model for intrinsic phonon-phonon scattering from isotropic to anisotropic. Combined with the anisotropic Debye dispersion, this anisotropic Klemens model leads to analytical expressions for heat transfer along both ab-plane (κab) and c-axis (κc), suitable for both layered and chainlike materials with any anisotropy ratio of the dispersion and the scattering. This combination of dispersion and scattering is further applied to the equation of phonon radiative transfer to model heat conduction across anisotropic thin films. The model is compared to experimental κab and κc of bulk graphite at high temperatures (T≥0.1×max(θD,ab,θD,c), where θD,ab and θD,c are the two Debye temperatures), leading to best-fit scattering parameters that capture the harmonic and anharmonic nature of the intra- and inter-layer bonding of graphite. With no further adjusting of these parameters, the anisotropic scattering model performs at least 9 times better than the isotropic one at explaining the experimental κc of graphite thin films. This size effect is further justified by comparing the accumulation function of κc.

A thermodynamic extremal principle incorporating the constraints from both fluxes and forces. I. Modeling

The dependencies of fluxes and forces were paid close attention to the phenomenological theory of Onsager. But in such a case, it seems that the Onsager’s reciprocal relations are not necessarily fulfilled. In this work, the problem of thermo-diffusion was chosen as an example and a combination of the first and the second law of thermodynamics was adopted to describe the reversible and the irreversible process. Accordingly, the Gibbs–Duhem relation was found to be followed by not only the equilibrium but also the non-equilibrium thermodynamics, i.e., the dependency of forces needs to be considered during the derivation of evolution equations. After that, a comparative study between the previous thermodynamic extremal principle (TEP) incorporating only the constraint from fluxes and the present TEP incorporating the constraints from both fluxes and forces was carried out. For the former, the well-known Dufour effect cannot be described, whereas, for the latter, both the well-known Soret effect and the Dufour effect can be predicted. Furthermore, the phenomenological equations were uniquely determined using the present TEP, and Onsager’s reciprocal relations were found to be followed, thus solving the problem of the n-fold arbitrariness for the kinetic coefficients pointed out previously. The present work not only extends the TEP to non-isothermal thermodynamics but also might provide guidance for modeling dissipation systems with constraints from both fluxes and forces.

Diffusiophoresis of Macromolecules within the Framework of Multicomponent Diffusion.

Diffusiophoresis is the isothermal migration of a colloidal particle through a liquid caused by a cosolute concentration gradient. Although diffusiophoresis was originally introduced using hydrodynamics, it can also be described by employing the framework of multicomponent diffusion. This not only enables the extraction of diffusiophoresis coefficients from measured multicomponent-diffusion coefficients but also their theoretical interpretation using fundamental thermodynamic and transport parameters. This review discusses the connection of diffusiophoresis with the 2 × 2 diffusion-coefficient matrix of ternary liquid mixtures. Specifically, diffusiophoresis is linked to the cross-term diffusion coefficient characterizing diffusion of colloidal particles due to cosolute concentration gradient. The other cross-term, which describes cosolute diffusion due to the concentration gradient of colloidal particles, is denoted as osmotic diffusion. Representative experimental results on diffusiophoresis and osmotic diffusion for polyethylene glycol and lysozyme in the presence of aqueous salts and osmolytes are described. These data were extracted from ternary diffusion coefficients measured using precision Rayleigh interferometry at 25 °C. The preferential-hydration and electrophoretic mechanisms responsible for diffusiophoresis are examined. The connection of diffusiophoresis and osmotic diffusion to preferential-interaction coefficients, Onsager reciprocal relations, Donnan equilibrium and Nernst-Planck equations are also discussed.

Graph theoretic analysis of three-terminal quantum dot thermocouples: Onsager relations and spin-thermoelectric effects

Graph theoretic analysis of three-terminal quantum dot thermocouples: Onsager relations and spin-thermoelectric effects

Gravito-thermal transports, Onsager reciprocal relation and gravitational Wiedemann-Franz law

Using the near-detailed-balance distribution function obtained in our recent work, we present a set of covariant gravito-thermal transport equations (i.e. the flow of various charges as linear response to thermodynamical forces) for neutral relativistic gases in a generic stationary spacetime. All relevant tensorial transport coefficients are worked out and are presented using some particular integration functions in (α,ζ), where α=−βμ and ζ=βm is the relativistic coldness, with β being the inverse temperature and μ being the chemical potential. It is shown that the Onsager reciprocal relation holds in the gravito-thermal transport phenomena, and that the heat conductivity and the gravito-conductivity tensors are proportional to each other, with the coefficient of proportionality given by the product of the so-called Lorenz number with the temperature, thus proving a gravitational variant of the Wiedemann-Franz law. It is remarkable that, for strongly degenerate Fermi gases, the Lorenz number takes a universal constant value L=π2/3, which extends the Wiedemann-Franz law into the Wiedemann-Franz-Lorenz law.

Thermodynamic Derivation of the Reciprocal Relation of Thermoelectricity.

The Kelvin relation, relating the Seebeck coefficient and the Peltier coefficient, is a theoretical basis of thermoelectricity. It was first derived by Kelvin using a quasi-thermodynamic approach. However, Kelvin's approach was subjected to much criticism due to the rude neglect of irreversible factors. It was only later that a seemingly plausible proof of the Kelvin relation was given using the Onsager reciprocal relation with full consideration of irreversibility. Despite this, a critical issue remains. It is believed that the Seebeck and Peltier effects are thermodynamically reversible, and therefore, the Kelvin relation should also be independent of irreversibility. Kelvin's quasi-thermodynamic approach, although seemingly irrational, may well have touched on the essence of thermoelectricity. To avoid Kelvin's dilemma, this study conceives the physical scenarios of equilibrium thermodynamics to explore thermoelectricity. Unlike Kelvin's quasi-thermodynamic approach, here, a completely reversible thermodynamic approach is used to establish the reciprocal relations of thermoelectricity, on the basis of which the Kelvin relation is once again derived. Moreover, a direct thermodynamic derivation of the Onsager reciprocal relations for fluxes defined as the time derivative of an extensive state variable is given using the method of equilibrium thermodynamics. The present theory can be extended to other coupled phenomena.

Thermodynamic ground and Berry-phase origin of the planar spin Hall effect

The thermodynamic ground of the spin transport is elaborated, demonstrating the Onsager's reciprocal relation. The latter is also confirmed by deriving the spin Hall effect and its inverse using the semiclassical theory and the linear response theory. Importantly, the intrinsic contribution to the spin conductivity that satisfies the Onsager's relation has only Hall-type component and hence does not dissipate heat, in analogy to the anomalous Hall effect and fulfilling the thermodynamic requirement. Based on the expression of the spin Hall conductivity, the Berry-phase origin is elaborated for the recent-discovered planar spin Hall effect which features current-induced spin polarization within the plane of the Hall deflection. We unravel a spin-repulsion vector governing the planar spin Hall effect, providing a transparent criteria for identifying intrinsic planar spin Hall materials. Finite spin-repulsion vector is found permitted in 13 crystalline point groups, revealing a big number of unexplored planar spin Hall systems. Our result can be used for the quantitative calculation of the planar spin Hall effect, facilitating further material hunting and experimental investigation. Published by the American Physical Society 2024

Mechanism for Electrostatically Generated Magnetoresistance in Chiral Systems without Spin-Dependent Transport.

Significant attention has been drawn to electronic transport in chiral materials coupled to ferromagnets in the chirality-induced spin selectivity (CISS) effect. A large magnetoresistance (MR) is usually observed, which is widely interpreted to originate from spin (dependent) transport. However, there are severe discrepancies between the experimental results and the theoretical interpretations, most notably the apparent failure of the Onsager reciprocity relations in the linear response regime. We provide an alternative mechanism for the two terminal MR in chiral systems coupled to a ferromagnet. For this, we point out that it was observed experimentally that the electrostatic contact potential of chiral materials on a ferromagnet depends on the magnetization direction and chirality. The mechanism that we provide causes the transport barrier to be modified by the magnetization direction, already in equilibrium, in the absence of a bias current. This strongly alters the charge transport through and over the barrier, not requiring spin transport. This provides a mechanism that allows the linear response resistance to be sensitive to the magnetization direction and also explains the failure of the Onsager reciprocity relations. We propose experimental configurations to confirm our alternative mechanism for MR.

Revisit nonequilibrium thermodynamics based on thermomass theory and its applications in nanosystems

Abstract The development of non-Fourier heat conduction models is encouraged by the invalidity of Fourier’s law to explain heat conduction in ultrafast or ultrasmall systems. The production of negative entropy will result from the combination of traditional nonequlibrium thermodynamics and non-Fourier heat conduction models. To resolve this paradox, extended irreversible thermodynamics (EIT) introduces a new state variable. However, real dynamics variables like force and momentum are still missing from nonequilibrium thermodynamics and EIT’s generalized force and generalized flux. Heat has both mass and energy, according to thermomass theory and Einstein’s mass-energy relation. The generalized heat conduction model containing non-Fourier effects was established by thermomass gas model. The thermomass theory reshapes the concept of the generalized force and flux, temperature, and entropy production in nonequilibrium thermodynamics and revisits the assumption for the linear regression of the fluctuations in Onsager reciprocal relation. The generalized heat conduction model based on thermomass theory has been used to study thermal conductivity, thermoelectric effect, and thermal rectification effect in nanosystems.