To improve the estimation of entropy reduction in the process of macromolecules synthesis in a living cell, we have focused on the protein synthesis. We have calculated the entropy reduction of protein synthesis based on the concept of physical entropy which is proposed by Zurek in the context of Kolmogorov entropy or algorithmic complexity. Our calculations show that the rate of this entropy reduction which could be generalized to other macromolecular synthesis, is not constant and depends on the cell size in a manner that larger cells are more efficient than smaller ones while the energy cost of the synthesis and consequently increasing entropy during this process is fixed. We estimate the optimal size of a cell as an upper bound which is imposed by the second law of thermodynamics. We will show that this bound is validated by empirical evidence including the maximum cell size found in nature. In addition, we will argue that these results supports the lipid world hypothesis of the origin of life which asserts that to start the life\\\'s cycle, a membrane is needed in order to separate life processes from non-living matter.

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