The principles of the thermodynamics of irreversible processes which occur in biological cells considered as open systems, have been reviewed and applied in order to describe a possible evolution of cells during aging. The main featrue of such an approach is that cells operating in a steady state, optimize their free energy production by lowering their entropy production which is kept to a minimum. Instabilities can however occur which can lead the cell from one steady state to another characterized by a lower production of entropy. Concomitantly, the level of errors or entropy of the system will increase. The process will continue and the cell will go from one state to another until a critical level is attained where the cell can not cope any more with keeping its organization and will die. The effect of stresses and mitosis have been also considered in this model. Such an approach stresses that cells can only subsist as a whole in certain states which are the result of the genetic constitution but also of the optimalization of cellular functions given their requirement in energy and the fluctuations from the environmental changes. In this respect, it reconciles both programmed and stochastic theories of aging.