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It has shown that the accelerated expansion of the FRW Universe can beexplained as the quest towards the holographic equipartition ($N_{sur} =N_{bulk}$), satisfies the expansion law $\frac{dV}{dt} = l_{P}^{2} \left(N_{sur} - \epsilon N_{bulk} \right)$, from which one can derive the Friedmannequation of the FRW Universe in Einstein gravity \cite{paddy2012jun}. Weintroduce a generic derivation of the expansion law from the generalized firstlaw of thermodynamics $-dE=TdS$ and $dE=TdS + WdV$. The generic derivationprovides an expression for $N_{sur}$ in terms of entropy $S$ and the expansionlaw consistent with gravity theories having different entropy $S$, likeGauss-Bonnet and more general Lovelock gravity. We extended the same idea tothe non-equilibrium situation and obtained the expansion law in f(R) gravity asa specific case. For this, we used the first law of thermodynamics innon-equilibrium description having the extra entropy production term $Td_{i}S.$

Emergence of space from non-equilibrium thermodynamics in f(R) gravity