A self-gravitating system usually shows a quasi-universal density profile, such as the NFW profile of a simulated dark matter halo, the flat rotation curve of a spiral galaxy, the Sérsic profile of an elliptical galaxy, the King profile of a globular cluster and the exponential law of the stellar disk. It will be interesting if all of the above can be obtained from first principles. Based on the original work of White & Narayan (1987), we propose that if the self-bounded system is divided into infinite infinitesimal subsystems, the entropy of each subsystem can be maximized, but the whole system's gravity may just play the role of the wall, which may not increase the whole system's entropy St, and finally St may be the minimum among all of the locally maximized entropies (He & Kang 2010). For spherical systems with isotropic velocity dispersion, the form of the equation of state will be a hybrid of isothermal and adiabatic (Kang & He 2011). Hence this density profile can be approximated by a truncated isothermal sphere, which means that the total mass must be finite and our results can be consistent with observations (Kang & He 2011b). Our method requires that the mass and energy should be conserved, so we only compare our results with simulations of mild relaxation (i.e. the virial ratio is close to -1) of dissipationless collapse (Kang 2014), and the fitting also is well. The capacity can be calculated and is found not to be always negative as in previous works, and combining with calculations of the second order variation of the entropy, we find that the thermodynamical stability still can be true (Kang 2012) if the temperature tends to be zero. However, the cusp in the center of dark matter halos can not be explained, and more works will continue.

The above work can be generalized to study the radial distribution of the disk (Kang 2015). The energy constraint automatically disappears in our variation, because angular momentum is much more important than energy for the disk-shape system. To simplify this issue, a toy model is taken: 2D gravity is adopted, then at large scale it will be consistent with a flat rotation curve; the bulge and the stellar disk are studied together. Then with constraints of mass and angular momentum, the calculated surface density can be consistent with the truncated, up-bended or standard exponential law. Therefore the radial distribution of the stellar disk may be determined by both the random and orbital motions of stars. In our fittings the central gravity is set to be nonzero to include the effect of asymmetric components.

Numerical simulations have shown that strong gravitational torque by non-axisymmetric components induce evolutionary processes such as redistribution of mass and angular momentum in the galactic disks and consequent change of chemical abundance profiles. If we hope to understand chemical evolution gradients and their evolution we must understand the secular processes and re-arrangement of material by non-axisymmetric components and vice-versa. The most obvious of these aforementioned non-axisymmetric components are bars - at least 2/3 of spiral galaxies host a bar, and possibly all disk galaxies have hosted a bar at some point in their evolution. While observationally it has been found that barred galaxies have shallower gas-phase metallicity gradients than non-barred galaxies, a complementary analysis of the stellar abundance profiles has not yet been undertaken. This is unfortunate because the study of both gas and stars is important in providing a complete picture, as the two components undergo (and suffer from) very different evolutionary process. We present here a pilot study of the gas and stellar metallicity and age distributions in a sample of barred and non-barred galaxies using 2D spectroscopic observations. We found that the majority of the stellar mass in our sample is composed of old (~10 Gyr) stars. This is true in the bulge and the disc region, even beyond two disc scalelengths. In the disc region, a larger fraction of young stars is present in the external parts of the disc compared with the inner disc. The disc growth is, therefore, compatible with a moderate inside-out formation scenario, where the luminosity-weighted age changes from ~10 Gyrs in the centre, to ~4 Gyrs at two disc scalelengths, depending upon the galaxy. However, the presence of substructure, like star forming rings, can produce stellar population trends that are not directly related with the growing of the disc but to the bar potential. In the disc region, the metallicity gradient always decrease with the radius. In the bulge region this is not always true and we find inverse metallicity gradients in several galaxies.