Thermodynamics and dynamics of systems with long-range interactions

Bouchet, Freddy; Gupta, Shamik; Mukamel, David

doi:10.1016/j.physa.2010.02.024

Cited by 172 publications

(223 citation statements)

References 70 publications

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“…More recently, quasistationary states have been observed in gravitational sheet models [7] and their existence has been argued to be generic for a large class of classical long-range systems [8]. Virtually all finite-system results in the field have been obtained by numerical techniques, supplemented by analytical calculations in the N → ∞ Vlasov continuum limit [5,[9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Long-time asymptotics of the long-range Emch-Radin model

Kastner¹

2012

Open Physics

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Abstract:The long-time asymptotic behaviour is studied for a long-range variant of the Emch-Radin model of interacting spins. We derive upper and lower bounds on the expectation values of a class of observables. We prove analytically that the time scale at which the system relaxes to equilibrium diverges with the system size N, displaying quasistationary nonequilibrium behaviour. This finding implies that, for large enough N, equilibration will not be observed in an experiment of finite duration. PACS

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Section: Introductionmentioning

confidence: 99%

Long-time asymptotics of the long-range Emch-Radin model

Kastner¹

2012

Open Physics

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“…Recent exploration of long-range interacting systems, and in particular, of their static and dynamic properties, has focussed on an analytically tractable and representative model called the Hamiltonian mean-field (HMF) model [13,34]. Long-range interacting (LRI) systems are those in which the inter-particle interaction potential decays slower than 1/r d , with d being the dimension of the embedding space [35,36,37,38,39]. Unlike short-range ones, LRI systems are intrinsically nonadditive, namely, they cannot be trivially divided into independent macroscopic subparts.…”

Section: The Model As a Long-range Interacting Systemmentioning

confidence: 99%

Spontaneous synchronisation and nonequilibrium statistical mechanics of coupled phase oscillators

Gherardini

Gupta

Ruffo

2018

Contemporary Physics

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Spontaneous synchronization is a remarkable collective effect observed in nature, whereby a population of oscillating units, which have diverse natural frequencies and are in weak interaction with one another, evolves to spontaneously exhibit collective oscillations at a common frequency. The Kuramoto model provides the basic analytical framework to study spontaneous synchronization. The model comprises limit-cycle oscillators with distributed natural frequencies interacting through a mean-field coupling. Although more than forty years have passed since its introduction, the model continues to occupy the centre-stage of research in the field of non-linear dynamics, and is also widely applied to model diverse physical situations. In this brief review, starting with a derivation of the Kuramoto model and the synchronization phenomenon it exhibits, we summarize recent results on the study of a generalized Kuramoto model that includes inertial effects and stochastic noise. We describe the dynamics of the generalized model from a different yet a rather useful perspective, namely, that of long-range interacting systems driven out of equilibrium by quenched disordered external torques. A system is said to be long-range interacting if the inter-particle potential decays slowly as a function of distance. Using tools of statistical physics, we highlight the equilibrium and nonequilibrium aspects of the dynamics of the generalized Kuramoto model, and uncover a rather rich and complex phase diagram that it exhibits, which underlines the basic theme of intriguing emergent phenomena that are exhibited by many-body complex systems.

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“…Violent relaxation based on f LB is a mean-field theory (cf., e.g., Chavanis & Ispolatov 2002;Bouchet et al 2010). It supposes that a mean gravitational potential field can be defined and that a thermodynamic equilibrium state of self-gravitating matter moving in this field can be achieved.…”

Section: Complete Exclusion In Violent Relaxationmentioning

confidence: 99%

Incomplete-exclusion statistical mechanics in violent relaxation

Treumann

Baumjohann

2013

A&A

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Violent relaxation was proposed half a century ago as responsible for non-collisional dynamics in gravitationally bound systems of extended celestial objects after reaching an equilibrium state that can be described thermodynamically. It is based on a complete spatial exclusion principle that formally leads to a distribution function resembling the Fermi distribution. We extend this theory to incomplete spatial exclusion by assuming that Fermi states can only be partially occupied. This is made possible by analogy to Fermi statistics. A new form of distribution function has been obtained. Formally it does not resemble the Fermi distribution. It consists of a difference of two Bose distributions but has the same properties as the Fermi distribution. Using it in the violent relaxation equation for the global gravitational potential extends the violent relaxation theory to incomplete exclusion. Though this refines violent relaxation theory, it does not resolve its basic deficiencies: the mass problem and those problems related to the mean field assumption.

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Thermodynamics and dynamics of systems with long-range interactions

Cited by 172 publications

References 70 publications

Long-time asymptotics of the long-range Emch-Radin model

Long-time asymptotics of the long-range Emch-Radin model

Spontaneous synchronisation and nonequilibrium statistical mechanics of coupled phase oscillators

Incomplete-exclusion statistical mechanics in violent relaxation

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