Does the stream power theory have a physical foundation?

The minimum entropy production principle (mEPP) for flow in a wide rectangular channel shows that the entropy production rate is equal to the unit stream power divided by the product of temperature and flow depth. Only for isothermal, steady, uniform flow is an extremum of the entropy production equivalent to an extremum of unit stream power. For a sediment-carrying channel, minimization of unit stream power provides a linear relation between channel slope and water depth. In agreement with published results, the unit stream power is shown to be constant rather than minimized by mEPP within accuracy provided by data. The entropy generation rate is minimized only when the flow is as deep as possible. For a specified volumetric flow rate, the entropy production rate for uniform flow is is less than that for an M2, M3, or S3 profile but greater than that for an M1, S1, or S2 profile.