  It is shown that instability of stringy matter near the event horizon of a
black hole (the spreading effect) can be characterized by the Lyapunov
exponents. The Kolmogorov-Sinai entropy is the sum of all the positive Lyapunov
exponents and equals to the inverse gravitational radius. Due to a replacement
of the configuration space of a string by its phase space at distance of order
of the string scale, the relation between the Kolmogorov-Sinai and
Bekenstein-Hawking entropies is established. The KS entropy of a black hole
measures the rate at which information about the state of a string collapsing
into the black hole is lost with time as it spreads over the horizon.
