Value and Information : A Profit Maximizing Strategy Lor Maxwell's Demon

Applications of Lagrange's method of undetermined multipliers in physics and economics suggest some analogies between the two disciplines. Applying Jaynes' approach to information theory reveals the long standing problem of Maxwell's demon in thermodynamics as a constrained optimization problem where information and energy are dual concepts. Temperature emerges as the energetic price of information. This approach highlights the economic features of the Maxwell demon discussed by 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 economics example is presented where generalized temperature measures informational efficiency in the sense of Grossman and Stiglitz