Lonely Planets and Lightweight Asteroids: A Statistical Mechanics Model for the Planetary Problem

In this paper we propose a notion of stability, which we call $$\varepsilon -N$$ ε - N -stability, for systems of particles interacting via Newton’s gravitational potential, and orbiting 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 N that guarantees the $$\varepsilon -N$$ ε - N -stability. With some judicious but not particularly optimized estimates, borrowed from the classical theory of equilibrium statistical mechanics, we show that our model has a good fit with the data observed in the Solar System, and it gives a reasonable interpretation of some of its global properties.

Thermostatistics of bosonic and fermionic Fibonacci oscillators

In this work, we first introduce some new properties concerning the Fibonacci calculus. We then discuss the thermostatistics of gas models of two-parameter deformed oscillators, called bosonic and fermionic Fibonacci oscillators, in the thermodynamical limit. In this framework, we analyze the behavior of two-parameter deformed mean occupation numbers describing the Fibonacci-type bosonic and fermionic intermediate-statistics particles. A virial expansion of the equation of state for the bosonic Fibonacci oscillators’ gas model is obtained in both two and three dimensions, and the first five virial coefficients are derived in terms of the real independent deformation parameters [Formula: see text] and [Formula: see text]. The effect of bosonic and fermionic [Formula: see text], [Formula: see text]-deformation on the thermostatistical properties of Fibonacci-type [Formula: see text], [Formula: see text]-boson and [Formula: see text], [Formula: see text]-fermion gas models are also discussed. The results obtained in this work can be useful for investigating some exotic quasiparticle states encountered in condensed matter systems.

GENUINE CORRELATIONS IN FINITE-SIZE SPIN SYSTEMS

Genuine multipartite correlations in finite-size XY chains are studied as a function of the applied external magnetic field. We find that, for low temperatures, multipartite correlations are sensitive to the parity change in the Hamiltonian ground state, given that they exhibit a minimum every time that the ground state becomes degenerate. This implies that they can be used to detect the factorizing point, that is, the value of the external field such that, in the thermodynamical limit, the ground state becomes the tensor product of single-spin states.