The entropy production rate reflects the dissipation of free energy in a nonequilibrium state, and it is necessary for many biological functions. Nevertheless, trivial systems can display large entropy production, and it is yet an open challenge to characterize the out-of-equilibrium states of living systems and their operational meaning. We present a way to decompose the entropy production rate of a system, capturing how much of it is generated from higher-order interactions between its components. Our method combines recent information-geometric decompositions of the entropy production rate with a hierarchical decomposition of forces into k -body stochastic interactions.