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This paper presents an observation that under reasonable conditions, many partial differential equations from mathematical physics possess three structural properties. One of them can be understand as a variant of the celebrated Onsager…

Mathematical Physics · Physics 2007-08-28 Wen-an Yong

In this work a generalization of Onsager-Machlup's theory of time-dependent thermal fluctuations of equilibrium systems is proposed, to the case in which the system relaxes irreversibly along a non-equilibrium trajectory that can be…

Statistical Mechanics · Physics 2009-08-05 M. Medina-Noyola

We provide numerical evidence that the Onsager symmetry remains valid for systems subject to a spatially dependent magnetic field, in spite of the broken time-reversal symmetry. In addition, for the simplest case in which the field strength…

Statistical Mechanics · Physics 2019-02-15 Rongxiang Luo , Giuliano Benenti , Giulio Casati , Jiao Wang

This article is concerned with the dynamics of a mixture of gases. Under the assumption that all the gases are isothermal and inviscid, we show that the governing equations have an elegant conservation-dissipation structure. With the help…

Mathematical Physics · Physics 2015-02-13 Zaibao Yang , Wen-An Yong , Yi Zhu

Fluctuation theorems establish deep relations between observables away from thermal equilibrium. Until recently, the research on fluctuation theorems was focused on time-reversal-invariant systems. In this review we address some newly…

Statistical Mechanics · Physics 2015-06-18 Chenjie Wang , D. E. Feldman

We provide a general macrostatistical formulation of nonequilibrium steady states of reservoir driven quantum systems. This formulation is centred on the large scale properties of the locally conserved hydrodynamical observables, and our…

Mathematical Physics · Physics 2009-11-11 Geoffrey L. Sewell

The first Kelvin relation that states the Peltier coefficient should be equal to the product of temperature and Seebeck coefficient is a fundamental principle in thermoelectricity. It has been regarded as an important application and direct…

Statistical Mechanics · Physics 2021-01-20 Yu-Chao Hua , Ti-Wei Xue , Zeng-Yuan Guo

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…

Fluid Dynamics · Physics 2013-12-31 Ajit Kumar Mahendra , Ram Kumar Singh

The Onsager principle provides a variational route to the phenomenological equations of dissipative dynamics through the minimization of the Rayleighian. We develop a covariant formulation of the Onsager principle for active systems,…

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…

Statistical Mechanics · Physics 2026-05-29 E. S. Benilov

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…

Statistical Mechanics · Physics 2009-06-15 Giovanni Gallavotti

The characterization of finite-time thermodynamic processes is of crucial importance for extending equilibrium thermodynamics to nonequilibrium thermodynamics. The central issue is to quantify responses of thermodynamic variables and…

Statistical Mechanics · Physics 2023-09-15 Yuki Izumida

We present a linear response theory that establishes the continuum-mechanical origin of Onsager reciprocity in colloidal motion. By decoupling hydrostatic and hydrodynamic stress, we show that Onsager reciprocal relations emerge from the…

Soft Condensed Matter · Physics 2026-05-05 Jerome Burelbach

By using recent developments for the Langevin dynamics of spatially asymmetric systems, we routinely generalize the Onsager-Machlup fluctuation theory of the second order in time. In this form, it becomes applicable to fluctuating…

Statistical Mechanics · Physics 2016-12-28 Roman Belousov , E. G. D. Cohen

Some models for developed turbulence are considered; they are shown to obey a large fluctuations theorem, and one among them also obeys a response reciprocity relation of Onsager's type. This illustrates and extends ideas and techniques…

chao-dyn · Physics 2008-02-26 Giovanni Gallavotti

It has recently been pointed out that Hamiltonian particle systems in constant magnetic fields satisfy generalized time-reversal symmetries that enable to prove useful statistical relationships based on equilibrium phase-space probability…

Statistical Mechanics · Physics 2021-02-24 Alessandro Coretti , Lamberto Rondoni , Sara Bonella

Periodic driving is used to operate machines that go from standard macroscopic engines to small non-equilibrium micro-sized systems. Two classes of such systems are small heat engines driven by periodic temperature variations and molecular…

Statistical Mechanics · Physics 2017-11-16 Somrita Ray , Andre C. Barato

For thermoelectric transport in the presence of a magnetic field that breaks time-reversal symmetry, a strong bound on the Onsager coefficients is derived within a general set-up using three terminals. Asymmetric Onsager coefficients lead…

Statistical Mechanics · Physics 2013-02-13 Kay Brandner , Keiji Saito , Udo Seifert

We study thermal and charge transport in a three-terminal setup consisting of one superconducting and two ferromagnetic contacts. We predict that the simultaneous presence of spin filtering and of spin- dependent scattering phase shifts at…

Mesoscale and Nanoscale Physics · Physics 2013-01-30 P. Machon , M. Eschrig , W. Belzig

In the recent progress in nonequilibrium thermodynamics, information has been recognized as a kind of thermodynamic resource that can drive thermodynamic current without any direct energy injection. In this paper, we establish the framework…

Statistical Mechanics · Physics 2016-11-22 Shumpei Yamamoto , Sosuke Ito , Naoto Shiraishi , Takahiro Sagawa