Order in Nature

We learned in the last chapter that the entropy, and thus the state of disorder or uniformity of the universe is increasing and yet looking more closely we do see that there are large pockets of exceptions. Indeed living systems exhibit a great deal of variety and non-uniformity: Biological systems actually seem to strive towards greater order and complexity in their structure and function. How is this consistent with the second law? Consider for example a living organism. It is certainly not a random, uniform, collection of molecules. Indeed from its conception to maturity it develops into a highly complex and ordered structure. Of course we recognize that it is not an isolated system to which the conclusion of the second law applies. In fact a living organism feeds, breathes, and dissipates heat and other waste products: It takes in ordered energy (nutrients) and dissipates disordered energy (heat) in such a way that although its entropy actually decreases, that of the whole "universe" (consisting of the organism plus environment) increases in accordance with the second law. Note that we have already seen a simple example of how the entropy of an open system can increase. A heat reservoir can lose heat to a freely expanding gas, decreasing the entropy of the reservoir while increasing that of the gas. The analogy here is: organism $=$ reservoir and environment $=$ gas. But there is a further important difference between a living organism and the other inorganic systems considered so far. A living organism is in fact not really in equilibrium because it continually requires an intake of nutrients, continually dissipates and often undergoes changes in size or shape. We can apply the second law (meant only for the end points of an equilibrium system) by taking a short time interval during which we may assume the organism to be in equilibrium (after its intake and dissipation). However we know that in the long run, if the organism was to try and maintain this equilibrium continuously (with no intake and/or dissipation) it would soon degenerate (die) and of course this would result in its highly organsied state decaying into disorder. Thus an out of equilibrium (or non-equilibrium) situation is actually required for living organisms to maintain their order and complexity! Therefore one can say that the order and complexity of living systems is possible because they are open systems that are far from equilibrium. By contrast to closed systems in equilibrium which evolve towards a state of "boring" uniformity where differences and irregularities are smoothened out, open systems that are out-of-equilibrium can evolve towards states that display macroscopic order and patterns. That is, the order that can arise in non-equilibrium states is dynamic and interesting in comparison to the uniform and uninteresting order of equilibrium states. The term dissipative structures (associated with Landauer and popularised by Prigogine) is sometimes used to describe non-equilibrium open systems which take in matter or energy, also dissipate matter and/or energy, and which display macroscopic structure or order not inherent at the microscopic level. Note that the inflow is necessary to maintain the system out of equilibrium while the dissipation is required for decreasing the entropy of the system (but of course increasing that of the environment much more). Dissipation is also essential to maintain stability by allowing excess energy or matter to be removed. If not, then small perturbations can cause the system to deviate significantly from its original state. (E.g. think of an ideal pendulum as opposed to one with some friction.) Living organisms are of course examples of dissipative structures, but their complexity makes them difficult to study directly. It is useful therefore to look at some simpler examples of dissipative structures in order to gain some insight into structure and pattern formation in out-of-equilibrium systems. Note that these examples of non-equilibrium pattern/structure formation are true examples of complex behaviour in the sense that the systems cannot be characterized by a few time-independent effective parameters as is the case for equilibrium thermodynamic systems that we studied in the last chapter (which display uniform, completely ordered or completely disordered behaviour depending on the phase of the substance).