Asymptotically additive families of functions and a physical equivalence problem for flows

We show that additive and asymptotically additive families of continuous functions with respect to suspension flows are physically equivalent. In particular, the equivalence result holds for hyperbolic flows. We also obtain an equivalence relation for expansive flows. Moreover, we show how this equivalence result can be used to extend the nonadditive thermodynamic formalism and multifractal analysis for flows.