  Chaos is present in most stellar dynamical systems and manifests itself
through the exponential growth of small perturbations. Exponential divergence
drives time irreversibility and increases the entropy in the system. A
numerical consequence is that integrations of the N-body problem unavoidably
magnify truncation and rounding errors to macroscopic scales. Hitherto, a
quantitative relation between chaos in stellar dynamical systems and the level
of irreversibility remained undetermined. In this work we study chaotic
three-body systems in free fall initially using the accurate and precise N-body
code Brutus, which goes beyond standard double-precision arithmetic. We
demonstrate that the fraction of irreversible solutions decreases as a power
law with numerical accuracy. This can be derived from the distribution of
amplification factors of small initial perturbations. Applying this result to
systems consisting of three massive black holes with zero total angular
momentum, we conclude that up to five percent of such triples would require an
accuracy of smaller than the Planck length in order to produce a
time-reversible solution, thus rendering them fundamentally unpredictable.
