Characterization of interactions conserving specific entropy

Characterize the elements of the class of interactions generating a C*-dynamics for which conservation of the specific entropy holds.

Background

The paper assumes that the dynamics generated by an interaction preserves specific entropy in order to derive entropy monotonicity and formulate its structural theory of dynamical steady states. Conservation is known for several regularity classes, including exponentially decaying interactions and certain diameter-decay classes, but the authors identify the general characterization within the full class of interactions generating a C*-dynamics as unresolved.