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The Law of Maximum Entropy Production

The crucial final piece to the puzzle that provides the nomological basis for spontaneous order production, for dissolving the postulates of incommensurability between physics and psychology and physics and biology, between thermodynamics and evoluton, is the answer to a question that classical thermodynamics never asked. The classical statement of the second law says that entropy will be maximized, or potentials minimized, but it does not ask or answer the question of which out of available paths a system will take to accomplish this end. The answer to the question is that the system will select the path or assembly of paths out of otherwise available paths that minimizes the potential or maximizes the entropy at the fastest rate given the constraints. This is a statement of the law of maximum entropy production the physical selection principle that provides the nomological explanation, as will be seen below, for why the world is in the order production business (Swenson, 1988, 1991, 1992, 1995; Swenson &Turvey, 1991).
    Note that the law of maximum entropy production is in addition to the second law. The second law says only that entropy is maximized while the law of maximum entropy production says it is maximized (potentials minimized) at the fastest rate given the constraints. Like the active nature of the second law, the law of maximum entropy production is intuitively easy to grasp and empirically demonstrate.
     Consider the case of the warm mountain cabin sitting in cold, snow-covered woods. The difference in temperature between the cabin and the woods constitutes a potential and the cabin woods system as a consequence will produce flows of energy as heat from the cabin to the woods, e.g., by conduction through the walls, through the crack under the door, and so on. The second law says that if the fire in the wood stove warming the cabin goes out then at some future time (perhaps by morning) the

temperature of the cabin and the woods will be the same, and the potential will have been minimized. What the second law does not say is which paths out of available paths the system will select to do this. The law of maximum entropy production says the system will select the assembly of paths out of available paths that minimize the potential at the fastest rate given the constraints.
Suppose the house is tight and heat is flowing to the outside primarily by conduction through the walls. Imagine now opening a window or a door which amounts to removing a constraint on the rate of dissipation. What we know intuitively, and can confirm by experiment, is that whenever a constraint is removed and a new path or drain is provided that increases the rate at which the potential is minimized the system will seize the opportunity. In addition, since the opened window, for example, will not instantaneously drain all the potential some will still be allocated to conduction through the walls. Each path will drain all that it can, the fastest (in this case the open window) procuring the greatest amount of potential with what is left going to the slower paths (in this case conduction through the walls). The point is that no matter what the specific conditions, or the number of paths or drains, the system will automatically select the assembly of paths from among those otherwise available so as to get the system to the final state, to minimize or drain the potential, at the fastest rate given the constraints. This is the essence of the law of maximum entropy production.

     Given what has already been discussed above, the reader may have already leaped to the correct conclusion. If the world selects those dynamics that minimize potentials at the fastest rate given the constraints, and if ordered flow is more efficient at reducing potentials than disordered flow, then the world will select order whenever it gets the chance. Theworld is in the order production business because ordered flow produces entropy faster than disordered flow (Swenson, 1988, 1991, 1992, 1995; Swenson & Turvey, 1991), and this means the world can be expected to

 THERMODYNAMICS, EVOLUTION, AND BEHAVIOR - 225

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