Introducing complex living things
Finally, we have reached what this book is about, the system whose movements and actions you wish to learn to govern. We are going to start playing our first more serious music here. But before doing that, we have to introduce the one idea that transforms what we have learned so far into an application to living things.
Living things add one more, just one more, conservation. It emerges from their complex interiors as an extension of chemistry. Living things reproduce their own kind from the potentials available to them. They truly act as production factories. But if reproduction, making their own kind, were the only process, they could exhaust a reachable universe of its available materials and energies, a thermodynamic impossibility. So we have to recognize that not only do they reproduce, that is they are or become "born", but they also "die", come apart, "dissolve". That comes about by a thermodynamically feasible process. So we say, as a thermodynamic proposition: The rate of change of living things is proportional to the population of living things, but the measure of proportionality is the difference between the rate of those who are newly born and those who die. (Or everyone does it! Everyone who is, is born and everyone who is, dies). Or the rate of change of living things is the difference between those who just have been born and those who were born a characteristic time ago (but now have died. Physics, you see once again, always only says simple things! The possibility of immigration is, of course, also assumed).
Why is this a conservation? Because each generation, in confronting the future - interacting through many collisions involved in maintaining its own operation - collects materials and has an energetic factory process to reproduce its next continuing generation. It is the peculiar result of a complex application of chemistry. It is a so-called renormalized process, one that is not obligatory in nature, but one that emerged out of life's primitive systems' chemistry. It is a conservation of generations, although a renormalized, only "temporary" conservation, because if the internal chemistry did not continue so reliably driven, the life process would quite easily have stopped. Instead it has persisted, evolved slowly, over the past 3.8 billion years. (And for those who wish to challenge that idea of a natural evolution, I am willing to respond to that challenge with a proposal. Pay for perhaps 3-4 years of experiments, and I will show you creation of life de novo in the laboratory in a best efforts contract! That's how close, I believe, we are to a fuller capture of understanding life's machinery and its startup machinery. Enough small talk, back to business).
What that new renormalized conservation represents is a physical splitting of the natural conservation of number and matter density. If, as it appears most commonly in nature, atomisms are not born and do not die (although pair creation and annihilation is one feasible high energy process of being born and dying), then matter density and number density are tightly tied. When you count number of oxygen atoms or molecules you are also counting mass of oxygen atoms or molecules. Those atomisms that can be born, grow, and die represent a split in that conservation. Conservation of mass and of number become different, separate. You then count population as number which reproduce. But you count mass as growth. Thus a farmer or cultivator can put energy and matter either into fattening up his/her herds or plant crops, or he/she can put them into more number of animals or plants. The processes split.
The net effect of that split is to produce changes in the equation of state and equations of change. Now, the equation of state deals in relations among energy, mass, action, and population number, and there is the one additional equation of change for population number.
The potential stores remain similar to what they were before, except that now there is a chemical potential carried aboard (and manufactured) as a genetic code; also part of our material-energy supplies may come from other living things as depots of convenience. We eat them or make things from them (or get eaten by them in turn).
That's all we have to say to introduce this lesson. Its time for making music.