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Thermodynamics, Chaos, and Complexity

Classical thermodynamics is characterized by two laws: first, the conservation of energy and secondly, the non-decrease of entropy in closed systems isolated from their environment. Examples include gas in a balloon, liquid cooling in a container, wood burning in a stove. Since all such phenomena moved from states of low to states of high entropy and were said to be irreversible, thermodynamics seemed to point to an "arrow of time" contrary to classical mechanics, for which all phenomena are reversible in time.Reversibility in classical mechanics means that if state A can go to state B, state B can go to state A: for example, planets can orbit `clockwise' or `counterclockwise` around the sun; another example...

By the end of the nineteenth century, it had been shown that classical thermodynamics could be reduced to classical mechanics via statistical mechanics. To do so one treats solids, liquids and gases as composed of atoms, and regards bulk properties such as pressure, temperature and volume as arising from the motion of atoms. Since the motion of atoms obeyed classical mechanics, thermodynamic properties could be shown to be `epiphenomena,’ i.e., rooted in the underlying atomic motion. The reduction of classical thermodynamics also explained the apparent arrow of time as resulting from a system going from a complex, highly organized state, to a simple, disorganized state. Once again, fundamental physics was without an arrow of time.

During the twentieth century, non-linear, non-equilibrium systems were studied. These open systems exchange matter and/or energy with their larger environment, and in doing so, they can move from a less ordered to a more ordered state. The process decreases their entropy without violating the Second Law, since the total entropy of the system plus its environment increases in accordance with the Second Law. This phenomena is frequently called "order out of chaos" and such systems are called "dissipative systems." Does this reintroduce an arrow of time? It does phenomenologically, but whether it does so at a fundamental level is still an open question, since the underlying laws governing the atoms of these systems reflect temporal reversibility.

Recently there has been extensive study of systems obeying classical physics (e.g.., mechanics, meteorology, hydrodynamics, animal populations, etc.) and called chaotic, complex and self-organizing systems. These systems display an incredible sensitivity to their environment, epitomized in the famous "butterfly" effect where a small perturbation in, say, Nairobi effects the weather some weeks later in, say, Kyoto. Even in the simplest cases, chaotic systems appear entirely random even though they are governed by a deterministic equation.For example, the famous "logistic" equation can generate data which passes any known mathematical test for genuinely random data (for example, the sequence of numbers generated by the logistic... "Chaotic randomness" is thus a combination of phenomenologically random data governed by an entirely deterministic equation. On the one hand, it allows us to increasingly bring into the deterministic framework of classical science broad areas of phenomena which seemed to resist such inclusion. On the other hand, it represents a limit to the complete testability of the classical paradigm. This is because the practical limitations on predictability means we cannot rule out the possibility that certain macroscopic phenomena may in fact be genuinely random (not in fact governed by a deterministic equation). Meanwhile, chaos, self-organization and complexity theory help to explain how biological complexity arose in conformity with thermodynamics, and they give tacit support to the hope of some scholars that nature at the macroscipic level may in fact be ontologically open.

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Thermodynamics, Chaos, and Complexity

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Dr. Robert J. Russell


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