Fluctuations and response from a Hatano and Sasa approach

In this commentary paper, we present some of the main ideas on deriving a modified fluctuation-dissipation theorem off equilibrium, which in the end can all be related to an approach based on a generalized Hatano-Sasa relation. This generalized Hatano?Sasa relation also contains an interesting inequality, which can be viewed as a generalization of the second law of thermodynamics to transitions between non-equilibrium states.