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Summary

This chapter employs the theory comprising the principle of maximum entropy (POME) and the principle of minimum energy dissipation or its simplified minimum stream power for deriving hydraulic geometry relations. The theory leads to four families of downstream hydraulic geometry relations and eleven families of at-a-station hydraulic geometry relations. The principle of minimum energy dissipation rate states that the spatial variation of the stream power of a channel for a given discharge is accomplished by the spatial variation in channel form (flow depth and channel width) and hydraulic variables, including energy slope, flow velocity, and friction.

Boltzmann’s most probable distribution method is applied to derive the Polytomous Rasch model as the distribution accounting for the maximum number of possible outcomes in a test while introducing latent traits, item characteristics, and thresholds as constraints to the system. Affinities and similarities of the present result with other derivations of the model are discussed in light of the conceptual frameworks of statistical physics and of the principle of maximum entropy.

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20 - Minimum Energy Dissipation and Maximum Entropy Theory

Summary

A Derivation of the Polytomous Rasch Model Based on the Most Probable Distribution Method

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20 - Minimum Energy Dissipation and Maximum Entropy Theory

Summary

A Derivation of the Polytomous Rasch Model Based on the Most Probable Distribution Method