  Motivated by various applications and examples, the standard notion of
potential for dynamical systems has been generalized to almost additive and
asymptotically additive potential sequences, and the corresponding
thermodynamic formalism, dimension theory and large deviations theory have been
extensively studied in the recent years. In this paper, we show that every such
potential sequence is actually equivalent to a standard (additive) potential in
the sense that there exists a continuous potential with the same topological
pressure, equilibrium states, variational principle, weak Gibbs measures, level
sets (and irregular set) for the Lyapunov exponent and large deviations
properties. In this sense, our result shows that almost and asymptotically
additive potential sequences do not extend the scope of the theory compared to
standard potentials, and that many results in the literature about such
sequences can be recovered as immediate consequences of their counterpart in
the additive case. A corollary of our main result is that all quasi-Bernoulli
measures are weak Gibbs.
