Patterns of Maximal Entropy
The interplay between energy and entropy governs the equilibrium structure of macroscopic systems. At low temperatures, it is usually energetic considerations that are important while at higher excitation entropic aspects are more evident. One purpose of the maximum entropy formalism [1–4] is to extend the range of applications of this way of analysis. Must the system be at equilibrium?, must it be macroscopic?, must the relevant variable be energy and is there just one such relevant variable are some of the questions worth considering. The advantages of such an extension are clear in that a whole range of systems and phenomena, many of current interest, could be examined by methods analogous to those of equilibrium statistical mechanics [1,2]. The required generalization is that the state of the system is one of maximal entropy subject to constraints. When the value of the constraints (or ‘relevant variables’) already very much restrict the possible states, the state of the system is primarily specified by them. When many states are consistent with the given constraints, maximizing the entropy amongst that subset of states does serve to specif) the one. The generalization does therefore subsume equilibrium statistical mechanics and can indeed be used as a unifying principle for it [1,2,5].
KeywordsLagrange Multiplier Cluster Size Distribution Equilibrium Statistical Mechanic Occupied Cell Energetic Consideration
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