2016
DOI: 10.1016/j.physleta.2015.10.042
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Ergodicity in a two-dimensional self-gravitating many-body system

Abstract: We study the ergodic properties of a two-dimensional self-gravitating system using molecular dynamics simulations. We apply three different tests for ergodicity: a direct method comparing the time average of a particle momentum and position to the respective ensemble average, sojourn times statistics and the dynamical functional method. For comparison purposes they are also applied to a short-range interacting system and to the Hamiltonian mean-field model. Our results show that a two-dimensional self-gravitat… Show more

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Cited by 11 publications
(11 citation statements)
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“…On the other hand if dynamics is adiabatic -which is the case for the initial particle distributions that satisfy GVC -then α = 0.4, which is close to the exponent found for non-interacting particles. It will be interesting to explore how universal are these exponents by studying other long range systems, such as magnetically confined plasmas [15] or self-gravitating clusters [16][17][18][19]. The fact that the paramagnetic resonances and chaotic dynamics diminish significantly the entropy production time suggests that for short range interacting systems, for which dynamics is highly non-linear and chaotic, the exponent α → 0, and the entropy production will take place on a microscopic time scale even in the thermodynamic limit.…”
Section: Discussionmentioning
confidence: 99%
“…On the other hand if dynamics is adiabatic -which is the case for the initial particle distributions that satisfy GVC -then α = 0.4, which is close to the exponent found for non-interacting particles. It will be interesting to explore how universal are these exponents by studying other long range systems, such as magnetically confined plasmas [15] or self-gravitating clusters [16][17][18][19]. The fact that the paramagnetic resonances and chaotic dynamics diminish significantly the entropy production time suggests that for short range interacting systems, for which dynamics is highly non-linear and chaotic, the exponent α → 0, and the entropy production will take place on a microscopic time scale even in the thermodynamic limit.…”
Section: Discussionmentioning
confidence: 99%
“…for systems with long range interactions [118,119], where U ( r) is the potential between the particles and the integration is performed over all space.…”
Section: The Kinchin Theorem and Ergodicitymentioning
confidence: 99%
“…Similar questions have also been put forward in the context of selfgravitating matter, where regularizations appear naturally [43]. Allowing regularizations is also crucial when comparing theoretical results with numerical simulations (such as [56,29]) to ensure that the concavity of S(e) is a robust feature of the models in question. The main aim of the present work is to establish the concavity of S(e) for a rich class of potentials W, V and priors µ 0 , including the point-vortex model in R 2 , as well as its regularizations and regularized plasmas and self-gravitating systems in 2D and power-laws.…”
mentioning
confidence: 87%