The thermodynamic models available in the literature predict that during self-organizing processes the entropy of a cell considered as an open thermodynamic system decreases. This prediction leads to conclusion that cell imports a certain amount of negative entropy and generates entropy during irreversible metabolic processes. The controversial concept of negentropy was criticized recently. In this research a new model was proposed that is not based on the steady-state approximation and describes living systems more realistically. The analysis of the suggested model of an open thermodynamic system far from equilibrium, led to the conclusion that the entropy during self-organizing processes increases during growth (of a molecule or a cell). Using as models the synthesis of an oligopeptide and a growing hydrocarbon chain, it was shown that entropy of an open thermodynamic system increases during addition of monomers (a self-organizing process). A derived equation confirms the results obtained by calculations with literature experimental values of molar entropy. The decrease of entropy observed in self-organizing processes occurred only during phase transition. Prigogine's model demands a real life version of Maxwell demon to play its role in entropy reduction of the cell. Maxwell's demon has an ability to decrease entropy of a thermodynamic system, thus violating the second law of thermodynamics. Real life version of Maxwell's demon is believed to play a role in evolution [14,15], and possibly in abiogenesis [14][15][16][17]. This presents a problem for the RNA world abiogenesis theory. Living cells are for Davies, dissipative, open, and far-from-equilibrium systems that lower their entropy utilizing an influx of energy and molecular material in a multi-compartment structure with specific functional characteristics [18].Oppositely, Silva [19] reported that entropy of the organism increases in time. Gems and Doonan [20] published similar results that the entropy of the C. elegans pharynx tissues increases as the animal ages (and organizes itself). Hansen [11][12][13] Frenkel [21], Schneider and Key [22], and Michaelian [23] reported that change of entropy of an open thermodynamic system during self-organizing processes does not have to decrease. Toussaint [24][25][26] reported that rate of the entropy production (dS/dt) decreases during aging (in time). So the entropy itself increases, but the rate of its production decreases during life. Hayflick [27][28][29] describes the role of entropy increase in aging process.The aim of this research is to consider the general behavior of an open thermodynamic system out of equilibrium, and then to analyze the behavior of a cell as a real-life example of an open thermodynamic system. Having in mind the growth of real organisms it seems reasonable to develop a model that is not based on the steady state approximation.