Value and Information -- A Profit Maximizing Strategy for Maxwell's Demon

Applications of Lagrange's method of undetermined multipliers in physics and economics suggest some analogies between the two disciplinces. By using the work of E. T. Jaynes on information theory, the long standing problem of Maxwell's demon in thermodynamics can be cast as a constrained optimization problem where information and energy are dual concepts. Temperture emerges as the energetic price of information. This approach to the problem of the Maxwell demon highlights the economic features discussed byu Bridgman. It also suggests that an analog to temperature (or the price of information) should be present in any optimization problem constrained by costly information. A trivial economic example of this is discussed