  In this paper, we study the thermodynamic quantities of
Friedmann-Robertson-Walker (FRW) universe by using the tunneling formalism
beyond semiclassical approximation developed by \emph{Banerjee} and
\emph{Majhi}\cite{beyond0}. For this we first calculate the corrected
Hawking-like temperature on apparent horizon by considering both scalar
particle and fermion tunneling. With this corrected Hawking-like temperature,
the explicit expressions of the corrected entropy of apparent horizon for
various gravity theories including Einstein gravity, Gauss-Bonnet gravity,
Lovelock gravity, $f(R)$ gravity and scalar-tensor gravity, are computed. Our
results show that the corrected entropy formula for different gravity theories
can be written into a general expression (\ref{entropy-final}) of a same form.
It is also shown that this expression is also valid for black holes. This might
imply that the expression for the corrected entropy derived from tunneling
method is independent of gravity theory, spacetime and dimension of the
spacetime. Moreover, it is concluded that the basic thermodynamical property
that the corrected entropy on apparent horizon is a state function is satisfied
by the FRW universe.
