Irreversibility by competition on a Glauber-Ising model by means of the entropy production.

An out of equilibrium Ising model subjected to an irreversible dynamics is analyzed by means of a stochastic dynamics, on a effort that aims to understand the observed critical behavior as consequence of the intrinsic microscopic characteristics. The study focus on the kinetic phase transitions that take place by assuming a lattice model with inversion symmetry and under the influence of two competing Glauber dynamics, intended to describe the stationary states using the entropy production, which characterize the system behavior and clarifies its reversibility conditions. Thus, it is considered a square lattice formed by two sublattices interconnected, each one of which is in contact with a heat bath at different temperature from the other. Analytical and numerical treatments are faced, using mean-field approximations and Monte Carlo simulations. For the one dimensional model exact results for the entropy production were obtained, though in this case the phase transition that takes place in the two dimensional counterpart is not observed, fact which is in accordance with the behavior shared by lattice models presenting inversion symmetry. Results found for the stationary state show a critical behavior of the same class as the equilibrium Ising model with a phase transition of the second order, which is evidenced by a divergence with an exponent µ ¼ 0:003 of the entropy production derivative.

A Galactic ring of minimum stellar density near the solar orbit radius

We analyse the secular effects of a long-lived Galactic spiral structure on the stellar orbits with mean radii close to the corotation resonance. By test-particle simulations and different spiral potential models with parameters constrained on observations, we verified the formation of a minimum with amplitude ∼30–40 per cent of the background disc stellar density at corotation. Such a minimum is formed by the secular angular momentum transfer between stars and the spiral density wave on both sides of corotation. We demonstrate that the secular loss (gain) of angular momentum and decrease (increase) of mean orbital radius of stars just inside (outside) corotation can counterbalance the opposite trend of exchange of angular momentum shown by stars orbiting the librational points L4/5 at the corotation circle. Such secular processes actually allow steady spiral waves to promote radial migration across corotation. We propose some pieces of observational evidence for the minimum stellar density in the Galactic disc, such as its direct relation to the minimum in the observed rotation curve of the Galaxy at the radius r ∼ 9 kpc (for R0 = 7.5 kpc), as well as its association with a minimum in the distribution of Galactic radii of a sample of open clusters older than 1Gyr. The closeness of the solar orbit adius to the corotation resonance implies that the solar orbit lies inside a ring of minimum surface density (stellar + gas). This also implies a correction to larger values for the estimated total mass of the Galactic disc, and consequently, a greater contribution of the disc componente to the inner rotation curve of the Galaxy.