Anomalous hydrodynamics with dyonic charge

TL;DR

This paper investigates how anomalies influence hydrodynamics when dyonic charges are present, revealing that both $E\cdot B$ and $E^2 - B^2$ terms are essential for thermodynamic consistency.

Contribution

It demonstrates that the local second law of thermodynamics constrains the anomaly structure in dyonic hydrodynamics, requiring specific terms for positive entropy production.

Findings

Both $E\cdot B$ and $E^2 - B^2$ terms are necessary in the anomaly.

The structure of the anomaly is constrained by thermodynamic laws.

Specific coefficients are identified for anomaly terms to ensure positive entropy production.

Abstract

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.