Non-equilibrium statistical mechanics in the general theory of relativity

Kandrup, Henry E.

doi:10.1016/0003-4916(84)90184-2

Cited by 26 publications

(58 citation statements)

References 17 publications

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“…This is the basis of the work of Balescu, Hakim and Kandrup (1,17,26) amongst others. These theories are said to be "on mass shell" since for each particle…”

Section: Introductionmentioning

confidence: 80%

Covariant Relativistic Statistical Mechanics of Many Particles

Schieve

2005

Found Phys

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In this paper the quantum covariant relativistic dynamics of many bodies is reconsidered. It is emphasized that this is an event dynamics. The events are quantum statistically correlated by the global parameter τ . The derivation of an event Boltzmann equation emphasizes this. It is shown that this Boltzmann equation may be viewed as exact in a dilute event limit ignoring three event correlations. A quantum entropy principle is obtained for the marginal Wigner distribution function. By means of event linking (concatenations) particle properties such as the equation of state may be obtained. We further reconsider the generalized quantum equilibrium ensemble theory and the free event case of the Fermi-Dirac and Bose-Einstein distributions, and some consequences. The ultrarelativistic limit differs from the non-covariant theory and is a test of this point of view.

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“…This is the basis of the work of Balescu, Hakim and Kandrup (1,17,26) amongst others. These theories are said to be "on mass shell" since for each particle…”

Section: Introductionmentioning

confidence: 80%

Covariant Relativistic Statistical Mechanics of Many Particles

Schieve

2005

Found Phys

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“…is released it then recovers the exact starting point of [18,19] (in the framework of general relativity) and [24]. The very nature of such functional independence on the N particle world lines is that at given global proper time τ the representation point is sufficient to uniquely determine the particle world lines.…”

Section: Lemma 23 the Physical Distribution Function N Satisfiesmentioning

confidence: 90%

“…In the work of Israel and Kandrup [18,19] this concept was reinforced and explicitly formulated. Such an idea lies at the heart of Eq.…”

Section: Wwwann-physorgmentioning

confidence: 99%

“…At the early stages the Brussels-Austin school [15,45] undertook systematic attempts (see [13] for a review) to generalize the Newtonian classical correlation dynamics to special relativity, which is built on the canonical formulation of relativistic dynamics of classical many-body systems [8] with the Hamiltonian, if necessary, including field degrees of freedom. Unfortunately, as pointed out by many authors especially in the notable critical analysis by Hakim [1], Israel and Kandrup [18], and Kandrup [19], to proceed along this theoretical line one may have to overcome a number of conceptual and technical difficulties. The most serious problems are regarding covariance of the theory and particularly covariance of the evolution of many-body systems.…”

Section: Relativistic Nonequilibrium Statistical Mechanics: Manifestlmentioning

confidence: 99%

“…The solution to this problem may solve the puzzle of the relativistic generalization of the Maxwell-Boltzmann distribution which is currently undergoing intensified debate [3,14,23]. Second, in [19] the (local) equilibrium was studied under the kinetic approximation. There, the principal problem of formulating many-body equilibrium [1] has not been attacked.…”

Section: Overview Of This Series Of Papersmentioning

confidence: 99%

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Manifestly covariant classical correlation dynamics I. General theory

Tian

2009

Ann. Phys.

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n this series of papers we substantially extend investigations of Israel and Kandrup on nonequilibrium statistical mechanics in the framework of special relativity. This is the first one devoted to the general mathematical structure. Basing on the action-at-a-distance formalism we obtain a single-time Liouville equation. This equation describes the manifestly covariant evolution of the distribution function of full classical many-body systems. For such global evolution the Bogoliubov functional assumption is justified. In particular, using the Balescu-Wallenborn projection operator approach we find that the distribution function of full many-body systems is completely determined by the reduced one-body distribution function. A manifestly covariant closed nonlinear equation satisfied by the reduced one-body distribution function is rigorously derived. We also discuss extensively the generalization to the general relativity especially an application to self-gravitating systems.Comment: 19 pages, 1 figure, substantially extende

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Manifestly covariant classical correlation dynamics II. Transport equations and Hakim equilibrium conjecture

Tian

2009

Ann. Phys.

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This is the second of a series of papers on special relativistic classical statistical mechanics. Employing the general theory developed in the first paper, we derive rigorously the relativistic Vlasov, Landau, and Boltzmann equations, respectively. The latter two equations advocate the Jüttner distribution as the equilibrium distribution. We thus, at the fully microscopic level, provide support for the recent numerical findings of Cubero and co-workers of the special relativistic generalization of the Maxwell-Boltzmann distribution. Furthermore, the present theory allows us to calculate rigorously various correlation functions at the relativistic many-body equilibrium. Therefore, we demonstrate that the relativistic many-body equilibrium conjecture of Hakim is justified.

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Non-equilibrium statistical mechanics in the general theory of relativity

Cited by 26 publications

References 17 publications

Covariant Relativistic Statistical Mechanics of Many Particles

Covariant Relativistic Statistical Mechanics of Many Particles

Manifestly covariant classical correlation dynamics I. General theory

Manifestly covariant classical correlation dynamics II. Transport equations and Hakim equilibrium conjecture

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