  We ask the question whether entropy accumulates, in the sense that the
operationally relevant total uncertainty about an $n$-partite system $A = (A_1,
\ldots A_n)$ corresponds to the sum of the entropies of its parts $A_i$. The
Asymptotic Equipartition Property implies that this is indeed the case to first
order in $n$, under the assumption that the parts $A_i$ are identical and
independent of each other. Here we show that entropy accumulation occurs more
generally, i.e., without an independence assumption, provided one quantifies
the uncertainty about the individual systems $A_i$ by the von Neumann entropy
of suitably chosen conditional states. The analysis of a large system can hence
be reduced to the study of its parts. This is relevant for applications. In
device-independent cryptography, for instance, the approach yields essentially
optimal security bounds valid for general attacks, as shown by Arnon-Friedman
et al.
