The Bekenstein bound is a limit to the amount of entropy a thermodynamical system can have. The bound is given by the following expression:
\begin{equation}
S \leq \frac{2 \pi k R E}{\hbar c}
\end{equation}
where $k$ is Boltzmann's constant, $R$ is the radius of a sphere that can enclose the given system, $E$ is the total mass–energy including any rest masses, $ħ$ is the reduced Planck constant and $c$ is the speed of light.

The equality is reached for Black Holes.

Now, a system is in thermodynamical equilibrium when the entropy of the system is in a maximum and the constrains of the system( like pressure, volume, etc.) are satisfied. In our daily live, when we consider thermodynamical systems the bound is never achieve; only thermodynamical processes at the scale of astronomical objects seem to satisfy it.

Why is the equality only achieved at certain scales?

Is it possible to characterize black hole formation from purely thermodynamic considerations? I would like to know if it make sense to think black hole formation as some kind of phase transition.

This post imported from StackExchange Physics at 2014-04-13 14:48 (UCT), posted by SE-user yess