Statistical Mechanics of Unbound Two Dimensional Self-Gravitating Systems

Abstract

We study, using both theory and molecular dynamics simulations, the relaxation dynamics of a microcanonical two dimensional self-gravitating system. After a sufficiently large time, a gravitational cluster of N particles relaxes to the Maxwell-Boltzmann distribution. The time to reach the thermodynamic equilibrium, however, scales with the number of particles. In the thermodynamic limit, $N\to \infty$ at fixed total mass, equilibrium state is never reached and the system becomes trapped in a non-ergodic stationary state. An analytical theory is presented which allows us to quantitatively described this final stationary state, without any adjustable parameters.

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Cited by in corpus (40)

• Nonequilibrium Statistical Mechanics of Systems with Long-Range Interactions: Ubiquity of Core-Halo Distributions
• Core-halo distribution in the Hamiltonian Mean-Field Model
• Quasi-stationary states in the self-gravitating sheet model
• Nonequilibrium stationary states of 3D self-gravitating systems
• Ergodicity Breaking and Parametric Resonances in Systems with Long-Range Interactions
• Scaling of the dynamics of homogeneous states of one-dimensional long-range interacting systems
• Self-consistent inhomogeneous steady states in Hamiltonian mean field dynamics
• Quasistationarity in a model of classical spins with long-range interactions
• Out-of-equilibrium phase transitions in the HMF model: a closer look
• Nonequilibrium phase transitions in systems with long-range interactions
• Linear response theory for long-range interacting systems in quasistationary states
• Dynamics and physical interpretation of quasi-stationary states in systems with long-range interactions
• Local thermodynamics and the generalized Gibbs-Duhem equation in systems with long-range interactions
• Random transitions described by the stochastic Smoluchowski-Poisson system and by the stochastic Keller-Segel model
• Surprises from quenches in long-range interacting systems: Temperature inversion and cooling
• Non-equilibrium Statistical Mechanics of Two-dimensional Vortices
• Formation and relaxation of quasi-stationary states in particle systems with power law interactions
• Relaxation dynamics of stochastic long-range interacting systems
• Caloric curves fitted by polytropic distributions in the HMF model
• Symmetry Breaking in d-Dimensional Self-gravitating Systems
• Collisional relaxation of two-dimensional self-gravitating systems
• Statistical mechanics of collisionless relaxation in a noninteracting system
• Phase transitions in simplified models with long-range interactions
• Overdamped dynamics of long-range systems on a one-dimensional lattice: Dominance of the mean-field mode and phase transition
• Statistical mechanics of self-gravitating systems: mixing as a criterion for indistinguishability
• Density profiles of a self-gravitating lattice gas in one, two, and three dimensions
• Lyapunov Exponent and Criticality in the Hamiltonian Mean Field Model
• Topology of Collisionless Relaxation
• Entropy production in systems with long range interactions
• Ensemble Inequivalence in Systems with Wave-Particle Interaction
• Entropy production and Vlasov equation for self-gravitating systems
• Conditions for predicting quasistationary states by rearrangement formula
• Double Lynden-Bell Structure of Low-Energy Quasi-Stationary Distributions in the Hamiltonian Mean-Field Model
• On the effectiveness of mixing in violent relaxation
• Dynamics to the universal structure of one-dimensional self-gravitating systems in the quasi-equilibrium state
• Universal structure of two and three dimensional self-gravitating systems in the quasi-equilibrium state
• Violent relaxation in one-dimensional self-gravitating system: deviation from the Vlasov limit due to finite-$N$ effect
• Classical Goldstone modes in Long-Range Interacting Systems
• Core-Halo Quasi-Stationary States in the Hamiltonian Mean-Field Model
• Predicting the Final Stationary State of Sheared 2D Euler Fluids