The minimum rate of entropy production, during the one‐dimensional freezing of a lamellar eutectic at velocityVhas been calculated using a well‐defined model. This principle is found to be equivalent to the maximum interface temperature principle at smallVbut not at largeV. Since it does not provide the correct relationship between lamellar spacing and freezing velocity over the entire experimental range, there is considerable doubt as to its physical significance when applied to this case.