Complexity, Dissipation, Information and Organization

Charles Bennet in his paper [1] addresses the following questions belonging to both statistical mechanics an the theory of computation:
- What is the proper measure of intrinsic complexity to apply to states of a physical system?
- What role does thermodynamic irreversibility play in enabling systems to evolve spontaneously toward states of high complexity?

The paper is technical, but its first part is very helpful for the basic understanding of concepts like organization, complexity and information content.

A fundamental problem of statistical mechanics is why dissipative systems (those in which entropy is continually being produced and removed to the surroundings) tend to undergo “self-organization”, a spontaneous increase of complexity, of which the most extreme example is the origin and evolution of life. The converse principle, stating that nothing interesting is likely to happen in a system at thermal equilibrium, is called “heat death”.

One could try to use thermodynamic potentials to characterize complexity and organization but, I spite of the well known ability of dissipative systems to lower their entropy at the expense of their surroundings, organization cannot be directly identified with thermodynamic potentials such as entropy or free energy: the human body is intermediate in entropy between a crystal and a gas; and a bottle of sterile nutrient has higher free energy, but lower subjective organization, than the bacterial culture it would turn into if inoculated with a single bacterium. This difference in free energy means that, even without the seed bacterium the transformation from nutrients to bacteria (albeit an improbable case of spontaneously biogenesis) is still vastly more probable than the reverse transformation, from bacteria to sterile, high free-energy nutrients. Another example is the crystallization of a long-lived supersaturated solution: although crystallization without the catalytic assistance of a seed crystal may be so slow as to be unobservable in practice, it is not thermodynamically forbidden, and is, in fact, overwhelmingly more probable than the reverse process.

Subjective organization seems to obey a “slow growth law” which states that, except by a lucky accident, organization cannot increase quickly in any deterministic or probabilistic process, but it can increase slowly. It is this law which forbids sterile nutrient form turning into bacteria in the laboratory, but allows a similar transformation over geological time. If the slow growth law is to be obeyed, the rapid multiplication of bacteria after inoculation must not represent much increase in organization, beyond that already present in the seed bacterium. This means that subjective organization is not addictive: 1 bacterium contains much more organization that 0 bacteria, but 2 sibling bacteria contain about the same amount as 1.

The apparent non-additivity of “organization” suggest another definition for it, namely as information content. The information content of an object can be defined as the number of bits required to specify it uniquely. For example, two large message-like objects (e.g. DNA molecules), if they happen to be identical, do not together contain significantly more information than one alone. Different definitions of information content that may or may not be useful to define organization in biological molecules are developed in the article.

[1] C. H. Bennett "Information, Dissipation, and the Definition of Organization", in Emerging Syntheses in Science David Pines ed., Santa Fe Institute, pp 297-313 (1985), Addison-Wesley (Reading, Massachusetts 1987). Scanned PDF File