ENTROPYLAW.COM

 
Figure 2. Further examples of potentials that follow from nonequilibrium distributions of energy. Whenever energy (in whatever form) is out of equilibrium with its surroundings, a potential exists for producing change.

that the world acts spontaneously to minimize. In addition to the temperature difference shown in Figure 2, Figure 3 shows some other examples of potentials. 

The Second Law as a Law of Disorder

The active, macroscopic nature of the second law presented a profound blow to the mechanical world view which Boltzmann attempted to save by reducing the second law to the stochastic collisions of mechanical particles, or a law of probability. Modeling gas molecules as colliding billiard balls, Maxwell had shown that nonequilibrium velocity distributions (groups of molecules moving at the same speed and in the same direction) would become increasingly disordered with each collision leading to a final state of macroscopic uniformity and maximum microscopic disorder. Boltzmann recognized this state as the state of maximum entropy (where the macroscopic uniformity and microscopic disorder corresponds to the obliteration of all field potentials). Given this, he argued, the second law was simply the result of the fact that in a world of mechanically colliding particles disordered states are the most probable. There are so many more possible disordered states than ordered ones that a system will almost always be found either in the state of maximum disorder, the macrostate with the greatest number of accessible microstates such as a gas in a box at equilibrium, or moving towards it. A dynamically ordered state, one with molecules moving "at the same speed and in the same direction" said Boltzmann (1886/1974, p. 20), "is the most improbable case conceivable...an infinitely improbable configuration of energy."
Although Boltzmann himself acknowledged that his hypothesis of the second law had only been demonstrated for the case of a gas in a box near equilibrium, the science of his

time (and up until quite recently) was dominated by linear, near-equilibrium or equilibrium thinking, and his hypothesis became widely accepted. What we understand today, in effect, is that the world is not a linear, near equilibrium system like a gas in a box, but is instead nonlinear and far-from equilibrium, and that neither the second law, nor the world itself is reducible to a stochastic collision function. As the next section outlines, rather than being infinitely improbable, we now can see that spontaneous ordering is the expected consequence of physical law.

The Law of Maximum Entropy Production, or Why the World is in the Order-Production Business

Active, end-directed behavior was introduced nomologically into the world with the second law, but it did not at all seem to be the right kind for biology and psychology. Particulary with Boltzmann's interpretation, as Fisher, among others, noted, the end-directedness of the second law seemed to run completely opposite the active, end-directedness manifested by living things which, given the fecundity principle are in the order production business. The problem was partly put aside in the middle of this century when Bertalanffy (e.g., 1952, p. 145) showed that "spontaneous order...can appear in [open] systems" (systems with energy flows running through them) by virtue of their ability to build their order by dissipating potentials in their environments. Along the same lines, pointing to the balance equation of the second law, Schröedinger (1945) popularized the idea of living things as a streams of order which like flames are permitted to exist away from equilibrium because they feed off "negentropy" (potentials) in their environments. These ideas were further popularized by Prigogine (e.g., 1978) who

 THERMODYNAMICS, EVOLUTION, AND BEHAVIOR - 221

 PREVIOUS

 ENTROPYLAW.COM

 NEXT