Frenesy: Time-symmetric dynamical activity in nonequilibria

We review the concept of dynamical ensembles in nonequilibrium statistical mechanics as specified from an action functional or Lagrangian on spacetime. There, under local detailed balance, the breaking of time-reversal invariance is quantified via the entropy flux, and we revisit some of the consequences for fluctuation and response theory. Frenesy is the time-symmetric part of the path-space action with respect to a reference process. It collects the variable quiescence and dynamical activity as function of the system's trajectory, and as has been introduced under different forms in studies of nonequilibria. We discuss its various realizations for physically inspired Markov jump and diffusion processes and why it matters a good deal for nonequilibrium physics. This review then serves also as an introduction to the exploration of frenetic contributions in nonequilibrium phenomena.