  Two particles, initially in a product state, become entangled when they come
together and start to interact. Using semiclassical methods, we calculate the
time evolution of the corresponding reduced density matrix $\rho_1$, obtained
by integrating out the degrees of freedom of one of the particles. To quantify
the generation of entanglement, we calculate the purity ${\cal P}(t)={\rm
Tr}[\rho_1(t)^2]$. We find that entanglement generation sensitively depends (i)
on the interaction potential, especially on its strength and range, and (ii) on
the nature of the underlying classical dynamics. Under general statistical
assumptions, and for short-scaled interaction potentials, we find that ${\cal
P}(t)$ decays exponentially fast if the two particles are required to interact
in a chaotic environment, whereas it decays only algebraically in a regular
system. In the chaotic case, the decay rate is given by the golden rule
spreading of one-particle states due to the two-particle coupling, but cannot
exceed the system's Lyapunov exponent.
