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Chaotic hypothesis: Onsager reciprocity and fluctuation-dissipation theorem  [PDF]
Giovanni Gallavotti
Physics , 1995, DOI: 10.1007/BF02174123
Abstract: It is shown that the "chaoticity hypothesis", analogous to Ruelle's principle for turbulence and recently introduced in statistical mechanics, implies the Onsager reciprocity and the fluctuation dissipation theorem in various models for coexisting transport phenomena.
Relaxation in finite and isolated classical systems: an extension of Onsager's regression hypothesis  [PDF]
Marcus V. S. Bonan?a
Physics , 2011, DOI: 10.1103/PhysRevE.85.031122
Abstract: In order to derive the reciprocity relations, Onsager formulated a relation between thermal equilibrium fluctuations and relaxation widely known as regression hypothesis. It is shown in the present work how such relation can be extended to finite and isolated classical systems. This extension is derived from the fluctuation-dissipation theorem for the microcanonical ensemble. The results are exemplified with a nonintegrable system in order to motivate possible applications to dynamical systems and statistical mechanics of finite systems.
Thermostats, chaos and Onsager reciprocity  [PDF]
Giovanni Gallavotti
Physics , 2008, DOI: 10.1007/s10955-008-9655-3
Abstract: Finite thermostats are studied in the context of nonequilibrium statistical mechanics. Entropy production rate has been identified with the mechanical quantity expressed by the phase space contraction rate and the currents have been linked to its derivatives with respect to the parameters measuring the forcing intensities. In some instances Green-Kubo formulae, hence Onsager reciprocity, have been related to the fluctuation theorem. However, mainly when dissipation takes place at the boundary (as in gases or liquids in contact with thermostats), phase space contraction may be independent on some of the forcing parameters or, even in absence of forcing, phase space contraction may not vanish: then the relation with the fluctuation theorem does not seem to apply. On the other hand phase space contraction can be altered by changing the metric on phase space: here this ambiguity is discussed and employed to show that the relation between the fluctuation theorem and Green-Kubo formulae can be extended and is, by far, more general.
Onsager reciprocity in premelting solids  [PDF]
S. S. L. Peppin,M. Spannuth,J. S. Wettlaufer
Physics , 2008, DOI: 10.1007/s10955-009-9699-z
Abstract: The diffusive motion of colloidal particles dispersed in a premelting solid is analyzed within the framework of irreversible thermodynamics. We determine the mass diffusion coefficient, thermal diffusion coefficient and Soret coefficient of the particles in the dilute limit, and find good agreement with experimental data. In contrast to liquid suspensions, the unique nature of premelting solids allows us to derive an expression for the Dufour coefficient and independently verify the Onsager reciprocal relation coupling diffusion to the flow of heat.
Violation of Onsager Reciprocity in Underdoped Cuprates ?  [PDF]
C. M. Varma,Victor M. Yakovenko,A. Kapitulnik
Physics , 2010,
Abstract: One of the canons of condensed matter physics is the Onsager Reciprocity principle in systems in which the Hamiltonian commutes with the time-reversal operator. Recent results of measurements of the Nernst coefficient in underdoped YBa_2Cu_30_{6+x}, together with the measurements of the anisotropy of conductivity and the inferred anisotropy of the thermopower, imply that this principle is violated. The probable violation and its temperature dependence are shown to be consistent with the Loop-current phase which has been directly observed in other experiments. The violation is related directly to the magneto-electric symmetry of such a phase in which an applied electric field generates an effective magnetic field at right angle to it and to the order parameter vector, and vice versa.
Onsager reciprocity relations without microscopic reversibility  [PDF]
D. Gabrielli,G. Jona-Lasinio,C. Landim
Physics , 1995, DOI: 10.1103/PhysRevLett.77.1202
Abstract: In this paper we show that Onsager--Machlup time reversal properties of thermodynamic fluctuations and Onsager reciprocity relations for transport coefficients can hold also if the microscopic dynamics is not reversible. This result is based on the explicit construction of a class of conservative models which can be analysed rigorously.
Onsager reciprocity principle for kinetic models and kinetic schemes  [PDF]
Ajit Kumar Mahendra,Ram Kumar Singh
Physics , 2013,
Abstract: Boltzmann equation requires some alternative simpler kinetic model like BGK to replace the collision term. Such a kinetic model which replaces the Boltzmann collision integral should preserve the basic properties and characteristics of the Boltzmann equation and comply with the requirements of non equilibrium thermodynamics. Most of the research in development of kinetic theory based methods have focused more on entropy conditions, stability and ignored the crucial aspect of non equilibrium thermodynamics. The paper presents a new kinetic model formulated based on the principles of non equilibrium thermodynamics. The new kinetic model yields correct transport coefficients and satisfies Onsager's reciprocity relationship. The present work also describes a novel kinetic particle method and gas kinetic scheme based on this linkage of non-equilibrium thermodynamics and kinetic theory. The work also presents derivation of kinetic theory based wall boundary condition which complies with the principles of non-equilibrium thermodynamics, and can simulate both continuum and rarefied slip flow in order to avoid extremely costly multi-scale simulation.
The Onsager reciprocity relation and generalized efficiency of a thermal Brownian motor

Gao Tian-Fu,Zhang Yue,Chen Jin-Can,

中国物理 B , 2009,
Abstract: Based on a general model of Brownian motors, the Onsager coefficients and generalized efficiency of a thermal Brownian motor are calculated analytically. It is found that the Onsager reciprocity relation holds and the Onsager coefficients are not affected by the kinetic energy change due to the particle's motion. Only when the heat leak in the system is negligible can the determinant of the Onsager matrix vanish. Moreover, the influence of the main parameters characterizing the model on the generalized efficiency of the Brownian motor is discussed in detail. The characteristic curves of the generalized efficiency varying with these parameters are presented, and the maximum generalized efficiency and the corresponding optimum parameters are determined. The results obtained here are of general significance. They are used to analyze the performance characteristics of the Brownian motors operating in the three interesting cases with zero heat leak, zero average drift velocity or a linear response relation, so that some important conclusions in current references are directly included in some limit cases of the present paper.
A generalization of Onsager's reciprocity relations to gradient flows with nonlinear mobility  [PDF]
A. Mielke,M. A. Peletier,D. R. M. Renger
Mathematics , 2015,
Abstract: Onsager's 1931 `reciprocity relations' result connects microscopic time-reversibility with a symmetry property of corresponding macroscopic evolution equations. Among the many consequences is a variational characterization of the macroscopic evolution equation as a gradient-flow, steepest-ascent, or maximal-entropy-production equation. Onsager's original theorem is limited to close-to-equilibrium situations, with a Gaussian invariant measure and a linear macroscopic evolution. In this paper we generalize this result beyond these limitations, and show how the microscopic time-reversibility leads to natural generalized symmetry conditions, which take the form of generalized gradient flows.
Verification of the Thomson-Onsager reciprocity relation for spin caloritronics  [PDF]
F. K. Dejene,J. Flipse,B. J. van Wees
Physics , 2014, DOI: 10.1103/PhysRevB.90.180402
Abstract: We investigate the Thomson-Onsager relation between the spin-dependent Seebeck and spin-dependent Peltier effect. To maintain identical device and measurement conditions we measure both effects in a single Ni$_{80}$Fe$_{20}$/Cu/Ni$_{80}$Fe$_{20}$ nanopillar spin valve device subjected to either an electrical or a thermal bias. In the low bias regime, we observe similar spin signals as well as background responses, as required by the Onsager reciprocity relation. However, at large biases, deviation from reciprocity occurs due to dominant nonlinear contribution of the temperature dependent transport coefficients. By systematic modeling of these nonlinear thermoelectric effects and measuring higher order thermoelectric responses for different applied biases, we identify the transition between the two regimes as the point at which Joule heating start to dominate over Peltier heating. Our results signify the importance of local equilibrium for the validity of this phenomenological reciprocity relation.
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