Asymmetric-hopping effective theory of current-carrying bulk steady states and their effective temperature

Current-induced phenomena are often obscured by Joule heating, and their steady states are difficult to analyze in large open systems. We introduce a translationally invariant asymmetric-hopping model as an effective bulk description of boundary-driven systems under current. In a minimal case, it corresponds to an open-system Hatano--Nelson model. In a minimal noninteracting realization, we find that the effective temperature rises linearly with current density in the weak-current regime. The model provides a useful tool for separating intrinsic current-induced effects from heating.