The frenetic origin of negative differential response

The Green-Kubo formula for linear response coefficients is modified when dealing with nonequilibrium dynamics. In particular, negative differential conductivities are allowed to exist away from equilibrium. We give a unifying framework for such a negative differential response in terms of the frenetic contribution in the nonequilibrium formula. It corresponds to a negative dependence of the escape rates and reactivities on the driving forces. Partial caging in state space and reduction of dynamical activity with increased driving cause the current to drop. These are time-symmetric kinetic effects that are believed to play a major role in the study of nonequilibria. We give various simple examples treating particle and energy transport, which all follow the same pattern in the dependence of the dynamical activity on the nonequilibrium driving, made visible from recently derived nonequilibrium response theory.