Entropy structures with continuous partitions of unity

Using only continuous partitions of unity, we provide equivalent definitions for the metric, topological and topological tail entropies and pressures of a continuous self-map of a compact set, as well as their conditional versions. A tail variational principle for these new definitions is proved. We extend Downarowicz’s notions of candidates and entropy structures to account for almost-increasing sequences of functions arising from the new definitions. Finally, we deduce a partial answer to a question raised by Newhouse.