12: Death and Dissipation

Figure 12.1
growth and acquisition

We are now close to the end of our cycle.

Since our cell must obey the basic laws of physics, it cannot evade the famous second law of thermodynamics. This effectively states that no system can maintain itself indefinitely.

Since our cell or entity must abide by the second law of thermodynamics, then it cannot indefinitely retain its entire stock of chemical components, which is its mechanical chemical energy, M. As in Figure 12.1, it must open its exit orifice. It must allow its waste products—its old and tired components—to be ejected. It must reduce its internal energy.

The number of chemical components now decreases in a set of reverse mechanical chemical interactions. And with that decrease in the physical number of components, both the system's internal energy and its entropy are decreasing.

And since this is the best of all possible cases—it is the ideal—the system loses no more components than are absolutely necessary. Thus the decrease in this specific system's internal energy and entropy, due entirely to this loss of components, are kept within our very strict bounds.

The situation with the open exit orifice parallels what happened earlier in this cycle when the entry one was open. As the cell rejects its old and tired components and lowers its own entropy, its internal energy, its stock of chemical components, and its mechanical chemical energy, the entropy in the surroundings—which receives those components—increases at exactly the same rate. Since one entropy is decreasing while another is increasing, the combined entropy within the universe as a whole remains, as always, at precisely the same value throughout. There is simply an exchange and interchange of mechanical chemical energy and a mass of components between the cell and its surroundings, while the cell's internal energy reduces and everything remains otherwise the same.

Since the number of molecular components within the cell is decreasing while the entropy in the universe at large is staying exactly the same, then we are maintaining the potential to repeat this same process, in the future, for an indefinite and infinite number of cycles.

At the end of this process, all the components from the previous cycle will have been removed, with only new components that were acquired in this current cycle remaining. The prototypical cell now closes the exit orifice, and we are ready for the next and final step in this reproductive circulation of the generations. We have successfully eliminated all the mass and mechanical chemical energy that was there in the previous cycle, with only that garnered in this current cycle remaining.

And as with the entry orifice, every cell and population will have its established duration and rate for emitting its mechanical chemical energy and resources, so establishing both specified quantities and intensities.

The maxim of dissipation

A mathematical aside

Since this is the ideal and limiting case in which all the molecules and all the chemical components are exactly replaced, without loss anywhere, then we have ∫dm = 0. This is a statement of the attending mechanical chemical energy.

In real biological populations, of course, at least some biological entities will die before they can replace their components, so that even mechanical chemical energy is subject to loss. So we instead have ∫dm < 0.

But what remains true for both real populations and this ideal one is that since mass and mechanical chemical energy is being lost in excretion and waste, we have a negative flux of that mass and mechanical chemical energy. This is a ‘convergence’ or negative divergence. Its value is ∇ • M < 0. In the fully general case, there will also be divergences when there is a positive flux as the population increases its mass and mechanical energy through its sundry metablic processes, and so that ∇ • M > 0. Since one of these processes succeeds the other, in regular fashion, we can represent them conjointly as ∇ • M → 0.

We can now bring our three pieces of information concerning mechanical chemical energy and the mass flux together as a statement for the general case of all possible biological populations, and governing their interaction with their surroundings. These three are: (1) M = nm̅; (2) ∇ • M → 0; and (3) ∫dm < 0.

We can render the three conditions we found in the above mathematical aside verbally as:

The first maxim of ecology

The maxim of dissipation [Darwin's theory of competition]

(A) Any entity that can lift a weight will be prevented from so doing; and/or (B) can be put to use for the same purpose. (C) No entity can lift a weight indefinitely.

Statement | Discussion