In living systems, it is crucial to study the exchange of entropy that plays a fundamental role in the understanding of irreversible chemical reactions. However, there are not yet works able to describe in a systematic way the rate of entropy production associated to irreversible processes. Hence, here we develop a theoretical model to compute the rate of entropy in the minimum living system. In particular, we apply the model to the most interesting and relevant case of metabolic network, the glucose catabolism in normal and cancer cells. We show, (i) the rate of internal entropy is mainly due to irreversible chemical reactions, and (ii) the rate of external entropy is mostly correlated to the heat flow towards the intercellular environment. The future applications of our model could be of fundamental importance for a more complete understanding of self-renewal and physiopatologic processes and could potentially be a support for cancer detection.

Lactic fermentation and respiration are important metabolic pathways on which life is based. Here, the rate of entropy in a cell associated to fermentation and respiration processes in glucose catabolism of living systems is calculated. This is done for both internal and external heat and matter transport according to a thermodynamic approach based on Prigogine's formalism. It is shown that the rate of entropy associated to irreversible reactions in fermentation processes is higher than the corresponding one in respiration processes. Instead, this behaviour is reversed for diffusion of chemical species and for heat exchanges. The ratio between the rates of entropy associated to the two metabolic pathways has a space and time dependence for diffusion of chemical species and is invariant for heat and irreversible reactions. In both fermentation and respiration processes studied separately, the total entropy rate tends towards a minimum value fulfilling Prigogine's minimum dissipation principle and is in accordance with the second principle of thermodynamics. The applications of these results could be important for cancer detection and therapy.

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