The Formal Statistical Theory of Transport Processes

McLennan, James A.

doi:10.1002/9780470143513.ch6

Cited by 69 publications

(65 citation statements)

References 29 publications

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“…This formal expression is a special case of the McLennan-Zubarev non-equilibrium ensemble (see [McL,Zu1,Zu2]). In this and the following sections we shall turn this formal argument into a rigorous construction.…”

Section: Large Time Limit I: Scattering Theorymentioning

confidence: 99%

Entropic fluctuations in quantum statistical mechanics—an introduction

Jakšić¹,

Ogata²,

Pautrat³

et al. 2012

Quantum Theory From Small to Large Scales

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Section: Large Time Limit I: Scattering Theorymentioning

confidence: 99%

Entropic fluctuations in quantum statistical mechanics—an introduction

Jakšić¹,

Ogata²,

Pautrat³

et al. 2012

Quantum Theory From Small to Large Scales

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“…As noticed in the Introduction we resort to the use of NESEF. According to the formalism, following Mori, Zwanzig and others [31,32,33,34,35,36], the Hamiltonian of the system under consideration is separated out in a so-called relevant partĤ 0 , consisting of the energy operators of the free degrees of freedom, andĤ ′ containing the interactions among them and the coupling with external sources and reservoirs. In our case herê…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…The formalism introduces the fundamental properties of historicity and irreversibility in the evolution of the nonequilibrium system where dissipative and pumping processes are under way. In terms of the dynamics generated by this full Hamiltonian the equations of evolution of the macroscopic state of the system are obtained in the framework of the NESEF-based nonlinear quantum kinetic theory [31,32,33,34,35,36,40,41,42,43]. We call the attention to the fact that the evolution equations are the quantum mechanical equations of motion averaged over the nonequilibrium ensemble, with the NESEF-kinetic theory providing a practical way of calculation.…”

mentioning

confidence: 99%

“…The microscopic state of the system is characterized by the full Hamiltonian of spins and lattice vibrations after going through Holstein-Primakov and Bogoliubov transformations [28,29,30]. On the other hand, the characterization of the macroscopic state of the magnon system is done in terms of the Thermo-Mechanical Statistics based on the framework of a Non-Equilibrium Statistical Ensemble Formalism (NESEF for short) [31,32,33,34,35,36]. Other modern approach consists in the use of Computational Modeling [37,38] (developed after Non-equilibrium Molecular Dynamics [39]).…”

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confidence: 99%

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Dynamics of a Bose-Einstein condensate of excited magnons

2013

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Abstract. The emergence of a non-equilibrium Bose-Einstein-like condensation of magnons in rf-pumped magnetic thin films has recently been experimentally observed. We present here a complete theoretical description of the non-equilibrium processes involved. It it demonstrated that the phenomenon is another example of the presence of a Bose-Einstein-like condensation in nonequilibrium many-boson systems embedded in a thermal bath, better referred-to as Fröhlich-Bose-Einstein condensation. The complex behavior emerges after a threshold of the exciting intensity is attained. It is inhibited at higher intensities when the magnon-magnon interaction drives the magnons to internal thermalization. The observed behavior of the relaxation to equilibrium after the end of the pumping pulse is also accounted for and the different processes fully described.

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“…By the above setting, the McLennan-Zubarev steady state distribution is given as follows [14,15,16,17,18].…”

Section: The Mclennan-zubarev Steady State Distributionmentioning

confidence: 99%

The McLennan–Zubarev steady state distribution and fluctuation theorems

Sano

2017

Physica A: Statistical Mechanics and its Applications

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The McLennan-Zubarev steady state distribution is studied in the connection with fluctuation theorems. We derive the McLennan-Zubarev steady state distribution from the nonequilibrium detailed balance relation. Then, considering the cumulant function or cumulant functional, two fluctuation theorems for entropy and for currents are proved. Using the fluctuation theorem for currents, the current is expanded in terms of thermodynamic forces. In the lowest order of the thermodynamic force, we find that the transport coefficient satisfies the Onsager's reciprocal relation. In the next order, we derived the correction term to the Green-Kubo formula.

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The Formal Statistical Theory of Transport Processes

Cited by 69 publications

References 29 publications

Entropic fluctuations in quantum statistical mechanics—an introduction

Entropic fluctuations in quantum statistical mechanics—an introduction

Dynamics of a Bose-Einstein condensate of excited magnons

The McLennan–Zubarev steady state distribution and fluctuation theorems

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