9.1: Problem Setup

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Page ID: 50210

Paul Penfield, Jr.
Massachusetts Institute of Technology via MIT OpenCourseWare

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Before the Principle of Maximum Entropy can be used the problem domain needs to be set up. In cases involving physical systems, this means that the various states in which the system can exist need to be identified, and all the parameters involved in the constraints known. For example, the energy, electric charge, and other quantities associated with each of the quantum states is assumed known. It is not assumed in this step which particular state the system is actually in (which state is “occupied”). Indeed it is assumed that we cannot ever know this with certainty, and so we deal instead with the probability of each of the states being occupied. In applications to nonphysical systems, the various possible events have to be enumerated and the properties of each determined, particularly the values associated with each of the constraints. In this Chapter we will apply the general mathematical derivation to two examples, one a business model, and the other a model of a physical system (both very simple and crude).