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Quantum Statistical Mechanical Derivation of Generalized Hydrodynamic Equations
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Differential conservation equations for the mass, momentum, and energy density operators for a 1-component simple fluid of Bose or Fermi particles with arbitrary pairwise interactions were derived in this article.Abstract:
Differential conservation equations are derived for the mass‐, momentum‐, and energy‐density operators for a 1‐component simple fluid of Bose or Fermi particles with arbitrary pairwise interactions. These equations are used in a statistical mechanical derivation of exact equations of motion for the expectations of these operators. The equations of motion are coupled to equations relating these expectations to the local temperature, chemical potential, and fluid velocity. The coupled equations are closed in the sense that the expectations and their thermodynamic conjugates listed above are the only unknowns, although some of the dependence in the equations on the conjugates is expressed only implicitly. The equations of motion are memory‐retaining nonlocal generalizations of the classical hydrodynamic equations and apply to a normal fluid arbitrarily far from equilibrium. The formalism is not carried as far as has the corresponding classical formalism because the local equilibrium expectation of the moment...read more
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Book
Foundations of statistical mechanics
TL;DR: In this paper, the authors discuss how statistical concepts enter the treatment of deterministic mechanical systems, with particular reference to trajectory instabilities and to the KAM theorem, and deal with large systems: the thermodynamic limit and the theory of infinite systems.
Journal ArticleDOI
Dissipation in many-body systems: A geometric approach based on information theory
Journal ArticleDOI
On the connection of nonequilibrium information thermodynamics with non-hamiltonian quantum mechanics of open systems
R.S Ingarden,A Kossakowski +1 more
TL;DR: A critical and improved version of the non-Hamiltonian quantum mechanics and nonequilibrium information thermodynamics is presented in this article, where it is shown that the latter is connected with the former through the set of macroscopical observables defining the additional conditions by maximization of information.
Journal ArticleDOI
From reversible quantum microdynamics to irreversible quantum transport
Jochen Rau,Berndt Müller +1 more
TL;DR: In this article, the transition from reversible microdynamics to irreversible transport can be studied very efficiently and systematically with the help of the so-called projection method, which is used to analyze the well-known rate and quantum Boltzmann equations, and as a new application, the derivation of a source term which accounts for the spontaneous creation of electronpositron pairs in strong fields.
Journal ArticleDOI
From Reversible Quantum Microdynamics to Irreversible Quantum Transport
Jochen Rau,Berndt Müller +1 more
TL;DR: In this paper, the transition from reversible microdynamics to irreversible transport can be studied very efficiently with the help of the so-called projection method, which is used to analyze the well-known rate and quantum Boltzmann equations, and present, as a new application, the derivation of a source term accounting for the spontaneous creation of electron-positron pairs in strong fields.
References
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Journal ArticleDOI
The Statistical Mechanical Theory of Transport Processes. IV. The Equations of Hydrodynamics
J. H. Irving,John G. Kirkwood +1 more
TL;DR: In this article, the contributions of intermolecular force to the stress tensor and heat current density are expressed as quadratures of the density and current density in the configuration space of a pair of molecules.
Journal ArticleDOI
Markoff Random Processes and the Statistical Mechanics of Time‐Dependent Phenomena. II. Irreversible Processes in Fluids
TL;DR: In this article, the authors apply the procedure developed in a previous paper of the same main title to the specific case of irreversible processes in fluids, where the gross variables are chosen to be a finite number of the plane-wave expansion coefficients of the local particle, momentum and energy densities.
Journal ArticleDOI
A Continued-Fraction Representation of the Time-Correlation Functions
TL;DR: In this paper, a continued fraction expansion of the Laplace transform of the time correlation functions is obtained, which enables us to express the generalized susceptibilities and the transport coefficients in terms of the static correlation functions of a set of quantities.
Book
An introduction to the theory of superfluidity
TL;DR: A classic from 1965, this book covers the main aspects of the theory of quantum liquids, including the elementary excitation spectrum, hydrodynamics, and kinetic phenomena as mentioned in this paper, and can be used as a guide for professors teaching quantum liquid theory or as a text for graduate students.