• Corpus ID: 219635991

Lonely planets and light belts: the Statistical Mechanics of Gravitational Systems

@article{Pinzari2020LonelyPA,
  title={Lonely planets and light belts: the Statistical Mechanics of Gravitational Systems},
  author={Gabriella Pinzari and Benedetto Scoppola and Alessio Troiani},
  journal={arXiv: Mathematical Physics},
  year={2020}
}
In this paper we propose a notion of stability, that we call $\varepsilon$-stability, for systems of particles interacting via Newton's gravitational potential, and orbiting around a much bigger object. For these systems the usual thermodynamical stability condition, ensuring the possibility to perform the thermodynamical limit, fails, but one can use as relevant parameter the maximum number of particles that guarantees the $\varepsilon$-stability. With some judicious but not particularly… 
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References

SHOWING 1-10 OF 41 REFERENCES
On the equilibrium statistical mechanics of isothermal classical self-gravitating matter
The canonical ensemble is investigated for classical self-gravitating matter in a finite containerΛ[d]⊂ℝd,d=3 and 2. Starting with modified gravitational interactions (smoothed-out singularity), it…
Addressing the statistical mechanics of planet orbits in the solar system
The chaotic nature of planet dynamics in the solar system suggests the relevance of a statistical approach to planetary orbits. In such a statistical description, the time-dependent position and…
Statistical mechanics of gravitational systems with regular orbits: rigid body model of vector resonant relaxation
I consider a self-gravitating, N-body system assuming that the N constituents follow regular orbits about the center of mass of the cluster, where a central massive object may be present. I calculate…
THE STATISTICAL MECHANICS OF PLANET ORBITS
The final ?giant-impact? phase of terrestrial planet formation is believed to begin with a large number of planetary ?embryos? on nearly circular, coplanar orbits. Mutual gravitational interactions…
Metric stability of the planetary N-body problem
The “solution” of the N-body problem (NBP) has challenged astronomers and mathematicians for centuries. In particular, the “metric stability” (i.e., stability in a suitable measure theoretical sense)…
Perihelia Reduction and Global Kolmogorov Tori in the Planetary Problem
We prove the existence of an almost full measure set of $(3n-2)$--dimensional quasi periodic motions in the planetary problem with $(1+n)$ masses, with eccentricities arbitrarily close to the…
Thermodynamic Instability of a System of Gravitating Fermions
We discuss the temperature-dependent Thomas-Fermi equation for a system of many fermions with gravitational interaction. According to a previous investigation this equation becomes exact in a…
The constitution of matter: Existence of thermodynamics for systems composed of electrons and nuclei
We establish the existence of the infinite volume (thermodynamic) limit for the free energy density of a system of charged particles, e.g., electrons and nuclei. These particles, which are the…
Statistical mechanics of the isothermal lane-emden equation
For classical point particles in a box Λ with potential energy H(N)=N−1(1/2) ∑i≠j=1NV(xi,xj) we investigate the canonical ensemble for largeN. We prove that asN→∞ the correlation functions are…
The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics
Starting with a “relativistic” Schrödinger Hamiltonian for neutral gravitating particles, we prove that as the particle numberN→∞ and the gravitation constantG→0 we obtain the well known…
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