  Time-Dependent Density Functional Theory is mathematically formulated through
non-linear coupled time-dependent 3-dimensional partial differential equations
and it is natural to expect a strong sensitivity of its solutions to variations
of the initial conditions, akin to the butterfly effect ubiquitous in classical
dynamics. Since the Schr\"odinger equation for an interacting many-body system
is however linear and mathematically the exact equations of the Density
Functional Theory reproduce the corresponding one-body properties, it would
follow that the Lyapunov exponents are also vanishing within a Density
Functional Theory framework. Whether for realistic implementations of the
Time-Dependent Density Functional Theory the question of absence of the
butterfly effect and whether the dynamics provided is indeed a predictable
theory was never discussed. At the same time, since the time-dependent density
functional theory is a unique tool allowing us the study of non-equilibrium
dynamics of strongly interacting many-fermion systems, the question of
predictability of this theoretical framework is of paramount importance. Our
analysis, for a number of quantum superfluid many-body systems (unitary Fermi
gas, nuclear fission, and heavy-ion collisions) with a classical equivalent
number of degrees of freedom ${\cal O}(10^{10})$ and larger, suggests that its
maximum Lyapunov exponents are negligible for all practical purposes.

Statistical Mechanics;Nuclear Theory;Quantum Physics