  We derive a unified expansion law for our universe from the first law of
thermodynamics on the apparent horizon, where entropic evolution depicts the
emergence of cosmic space. The derivation advances a general form for degrees
of freedom on the surface and bulk, which provides a natural generalization for
the expansion law proposed by Padmanabhan. The general expression for the
surface degrees of freedom differs from the natural expectation, $ N_{sur }= 4S
$ in the emergent gravity paradigm for general theories of gravity. The
derivation also provides justification for the selection of Gibbons-Hawking
temperature in the original expansion law and for the use of areal volume in
the non-flat FRW universe. Since the unified expansion law exclusively depends
on the form of entropy, the method is applicable to obtain the expansion law in
any gravity theory without any additional ad hoc assumptions. From the general
expansion law, we have obtained the expansion law corresponding to different
theories of gravity like (n+1) Einstein, Gauss-Bonnet, Lovelock, and
Horava-Lifshitz. We also obtained the expansion law for non-extensive entropy
like Tsallis entropy from the unified expansion law.
