  The Kolmogorov-Sinai (K-S) entropy is a central measure of complexity and
chaos. Its calculation for many-body systems is an interesting and important
challenge. In this paper, the evaluation is formulated by considering
$N$-dimensional symplectic maps and deriving a transfer matrix formalism for
the stability problem. This approach makes explicit a duality relation that is
exactly analogous to one found in a generalized Anderson tight-binding model,
and leads to a formally exact expression for the finite-time K-S entropy.
Within this formalism there is a hierarchy of approximations, the final one
being a diagonal approximation that only makes use of instantaneous Hessians of
the potential to find the K-S entropy. By way of a non-trivial illustration,
the K-S entropy of $N$ identically coupled kicked rotors (standard maps) is
investigated. The validity of the various approximations with kicking strength,
particle number, and time are elucidated. An analytic formula for the K-S
entropy within the diagonal approximation is derived and its range of validity
is also explored.
