Using the first law of thermodynamics, we propose a relation between the system entropy (S) and its IR (L) and UV () cutoffs. In addition, applying this relation to the apparent horizon of flat FRWuniverse, whose entropy meets the Rényi entropy, a new holographic dark energy model is addressed. Thereinafter, the evolution of the flat FRW universe, filled by a pressureless source and the obtained dark energy candidate, is studied. In our model, there is no mutual interaction between the cosmos sectors. We find out that the obtained model is theoretically powerful to explain the current accelerated phase of the universe. This result emphasizes that the generalized entropy formalism is suitable for describing systems including the long-range interactions such as gravity.
