  Holographic screens are the generalization of the event horizon of a black
hole in entropic force scheme, which are defined by setting Newton potential
$\phi$ constant, \textit{i. e.} $e^{2\phi}=c=$const. By demonstrating that the
integrated first law of thermodynamics is equivalent to the ($r-r$) component
of Einstein equations, We strengthen the correspondence between thermodynamics
and gravity. We show that there are not only the first law of thermodynamics,
but also kinds of phase transitions of holographic screens. These phase
transitions are characterized by the discontinuity of their heat capacities. In
(n+1) dimensional Reissner-Nordstr\"{o}m-anti-de Sitter (RN-AdS) spacetime, we
analyze three kinds of phase transitions, which are of the holographic screens
with Q=0 (charge), constant $\Phi$ (electrostatic potential) and non-zero
constant $Q$. In the Q=0 case, only the holographic screens with $0\le c<1$ can
undergo phase transition. In the constant $\Phi$ case, the constraints become
as $0\le c+16\tilde{\Gamma}^{2}\Phi^{2}<1$, where $\tilde{\Gamma}$ is a
dimensional dependent parameter. By verifying the Ehrenfest equations, we show
that the phase transitions in this case are all second order phase transitions.
In the constant $Q$ case, there might be two, or one, or no phase transitions
of holographic screens, depending on the values of $Q$ and $c$.
