The Entropy Paradox

An energy flow can lead to destruction (increase in entropy, e.g., a cannon ball) or organization (decrease in entropy, e.g., photosynthesis). The same quantity of energy can destroy a wall or kill a man; obviously the loss of information and negentropy is much greater in the second case. Energy and information are never equivalent.

The classical example of the mixing of gases in an isolated system shows us that there can be an increase in entropy without energy input from outside. The point is that E and S are both state functions in classical thermodynamics, but energy is intrinsically reversible whereas entropy is not. Entropy has the broken time symmetry of which Prigogine speaks. In other words, entropy has an energy term plus a time term that energy does not have.

If we assume that energy and mass are conservative quantities, it follows that energy and mass cannot change with time. They may transform to other types of energy and mass but the overall quantities remain the same, that is, they are reversible.

Entropy has an intrinsic temporal parameter. Energy obeys spatial and material constraints; entropy obeys spatial, material, and temporal constraints.

If history and the succession of events are of scientific relevance, the concept of state function should be revised at a higher level of complexity. The singularity of an event also becomes of particular importance: if a certain quantity of energy is spent to kill a caterpillar, we lose the information embodied in the caterpillar. But were this the last caterpillar, we should lose its unique genetic information forever. The last caterpillar is different from the ┬╗th caterpillar.

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 constraints of the biosphere itself. 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, the ratio of energy to stored information is clearly different. The information that led to an evolution and organization of the two types of system is not proportional to the flow of energy.

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 4 ('The death of the deer'): mass and energy do not change, whereas entropy does. There is an entropic 'watershed' between far from equilibrium (living) systems and classical systems (the dead deer or any inorganic - not living system). The essence of the living organism resides in its being a 'configuration of processes'.

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

It is important to study flows of energy and matter, quantities which are intrinsically conserved; it is also important to study entropy flows, an intrinsically evolutionary and nonconserved quantity. 'But if energy and mass are intrinsically conserved and entropy is intrinsically evolutionary, how can entropy be calculated on the

Figure 4 The death of the deer: the entropic watershed between living systems (deer alive) and classical systems (dead deer).

basis of energy and mass quantities (entropy paradox)?' This question is still unanswered and all we can do is to note that the ecodynamic viewpoint is different from that of classical physics and classical ecology.

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