  The dynamical description of correlated nuclear motion is based on a set of
coupled equations of motion for the one-body density matrix $\rho (11';t)$ and
the two-body correlation function $c_2(12,1'2';t)$, which is obtained from the
density-matrix hierarchy beyond conventional mean-field approaches by
truncating 3-body correlations. The resulting equations nonperturbatively
describe particle-particle collisions (short-range correlations) as well as
particle-hole interactions (long-range correlations). Within a basis of
time-dependent Hartree-Fock states these equations of motion are solved for
collective vibrations of $^{40}Ca$ at several finite thermal excitation
energies corresponding to temperatures $T=0-6$ MeV. Transport coefficients for
friction and diffusion are extracted from the explicit solutions in comparison
to the solutions of the associated TDHF, VUU, Vlasov or damped quantum
oscillator equations of motion. We find that the actual magnitude of the
transport coefficients is strongly influenced by partlicle-hole correlations at
low temperature which generate large fluctuations in the nuclear shape degrees
of freedom. Thermodynamically, the specific heat and the entropy of the system
as a function of temperature does not differ much from the mean-field limit
except for a bump in the specific heat around $T\simeq 4$ MeV which we
attribute to the melting of shell effects in the correlated system.
