The entropy paradox

Stories take place in a setting, the details of which are not irrelevant to the story. What happens in the biosphere, the story of life, depends on the biosphere constraints. Hence it is important to have global models of the biosphere in terms of space, time, matter, energy, entropy, information, and their respective relations.

If we consider the evolutionary transition from anaerobic to aerobic living systems, then the ratio of energy to stored information is clearly different. The information that led to evolution and the organization of the two types of system is not proportional to the flow of energy, due to dissipative losses that also introduces irreversibility.

Thus, entropy breaks the symmetry of time and can change irrespective of changes of energy—energy being a conservative and reversible property, whereas entropy is evolutionary and irreversible per se. The flow of a non-conservative quantity, negentropy, makes life go and the occurrence of a negentropic production term is just the point that differs from analysis based on merely conservative terms (energy and matter).

The situation is explained in Figure 3.1 "The death of the deer": mass and energy do not change, whereas entropy does. There is an "entropic watershed", a gradient, between far from equilibrium (living) systems and classical systems (the dead deer or any inorganic, non living system). The essence of the living organism resides in it being a "configuration of processes".

We may conclude that in far from thermodynamic equilibrium systems (biological and ecological) entropy is not a state function, since it has intrinsic evolutionary properties, strikingly at variance with classical thermodynamics.

Figure 3.1 The death of the Deer, an example showing the difference between a living, far from equilibrium system compared with the situation after its death where irreversible changes becomes dominant. (After Tiezzi, 2006b.)

It is important to study energy and matter flows, quantities that are intrinsically conserved; it is also important to study entropy flow, an intrinsically evolutionary and non-conserved quantity. But if energy and mass are intrinsically conserved and entropy is intrinsically evolutionary, how can entropy be calculated on the basis of energy and mass quantities (entropy paradox)? This question is still unanswered and all we can do is to note that the eco-dynamic viewpoint is different from that of classical physics and classical ecology.

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