Nonextensive Thermodynamics and Glassy behaviour in Hamiltonian systems

Abstract

An instructive and apparently simple model of fully-coupled rotators, the so-called Hamiltonian Mean Field (HMF) model, together with a generalized version with variable interaction range, have revealed a very complex out-of-equilibrium dynamics which can be considered paradigmatic for nonextensive systems. In this short paper we illustrate the interesting anomalous pre-equilibrium dynamics, focusing on the novel connections to the generalized nonextensive thermostatistics and the recent links to glassy systems.

9 pages, 5 figures. To be published by Europhysics News

References in corpus (1)

• Dynamics and Thermodynamics of a model with long-range interactions

Cited by in corpus (25)

• Nonadditive entropy: the concept and its use
• Exploring the thermodynamic limit of Hamiltonian models: convergence to the Vlasov equation
• Nonergodicity and Central Limit Behavior for Long-range Hamiltonians
• Lynden-Bell and Tsallis distributions for the HMF model
• Quasi-stationary states and incomplete violent relaxation in systems with long-range interactions
• Long time behavior of quasi-stationary states of the Hamiltonian Mean-Field model
• A closer look at the indications of q-generalized Central Limit Theorem behavior in quasi-stationary states of the HMF model
• Kinetic equations for systems with long-range interactions: a unified description
• A generalization of the central limit theorem consistent with nonextensive statistical mechanics
• Global fluctuations in physical systems: a subtle interplay between sum and extreme value statistics
• Hamiltonian and Brownian systems with long-range interactions: III. The BBGKY hierarchy for spatially inhomogeneous systems
• Central Limit Behavior in the Kuramoto model at the 'Edge of Chaos'
• Dynamical stability of systems with long-range interactions: application of the Nyquist method to the HMF model
• Inhomogeneous Tsallis distributions in the HMF model
• Analytic results for the Tsallis thermodynamic variables
• Deviation from Gaussianity in the cosmic microwave background temperature fluctuations
• Metastability in the Hamiltonian Mean Field model and Kuramoto model
• On the non-Boltzmannian nature of quasi-stationary states in long-range interacting systems
• Curious behaviour of the diffusion coefficient and friction force for the strongly inhomogeneous HMF model
• Thermodynamics of the HMF model with a magnetic field
• Effective spin-glass Hamiltonian for the anomalous dynamics of the HMF model
• On "Ergodicity and Central Limit Theorem in Systems with Long-Range Interactions" by Figueiredo et al
• Hamiltonian mean field model : effect of temporal perturbation in coupling matrix
• Non-equilibrium attractor for non-linear stochastic dynamics
• T. Dauxois' "Non-Gaussian distributions under scrutiny" under scrutiny