We study anomalous hydrodynamics with a dyonic charge. We show that the local
second law of thermodynamics constrains the structure of the anomaly in
addition to the structure of the hydrodynamic constitutive equations. In
particular, we show that not only the usual $E\cdot B$ term but also $E^2 -B^2$
term should be present in the anomaly with a specific coefficient for the local
entropy production to be positive definite.