Thermodynamics and dynamics of a 1-D gravitational system

Abstract

We describe a one-dimensional self-gravitating system derived from the problem of large-scale structure formation in cosmology. Considering small times so that the expansion can be neglected we present a thermodynamical analysis of this system. We find a second-order phase transition at $T_{c1}$ from an homogeneous equilibrium at high temperature to a clustered phase (with a density peak at one of the boundaries of the system) at low temperature. There also exists an infinite series of unstable equilibria which appear at lower temperatures $T_{cn}$, reflecting the scale-free nature of the gravitational interaction and the usual Jeans instability. We find that, as for the similar HMF (Hamiltonian mean field) model, all three micro-canonical, canonical and grand-canonical ensembles agree with each other, as well as with the stability properties associated with a hydrodynamical approach. On the other hand, the collisionless dynamics governed by the Vlasov equation yields the same results except that at low $T$ the equilibrium associated with two density peaks (one at each boundary) becomes stable.

16 pages, published in A&A

References in corpus (5)

• Dynamics and thermodynamics of a simple model similar to self-gravitating systems: the HMF model
• Hamiltonian and Brownian systems with long-range interactions
• A new approach to gravitational clustering: a path-integral formalism and large-N expansions
• A cloudy Vlasov solution
• The Self-Gravitating Gas in the Presence of Dark Energy: Monte-Carlo Simulations and Stability Analysis

Cited by in corpus (12)

• Nonequilibrium Statistical Mechanics of Systems with Long-Range Interactions: Ubiquity of Core-Halo Distributions
• Kinetic theory of long-range interacting systems with angle-action variables and collective effects
• Kinetic theory of spatially inhomogeneous stellar systems without collective effects
• Relaxation to thermal equilibrium in the self-gravitating sheet model
• 1-d gravity in infinite point distributions
• Phase transitions in self-gravitating systems and bacterial populations with a screened attractive potential
• Cosmology in One Dimension: Fractal Geometry, Power Spectra and Correlation
• Thermodynamics of a one-dimensional self-gravitating gas with periodic boundary conditions
• Gravitational force in an infinite one-dimensional Poisson distribution
• Ultra-local models of modified gravity without kinetic term
• Dynamics of One-dimensional Self-gravitating Systems Using Hermite-Legendre Polynomials
• One-Dimensional Relativistic Self-Gravitating Systems