  Highly excited many-particle states in quantum systems (nuclei, atoms,
quantum dots, spin systems, quantum computers) can be ``chaotic''
superpositions of mean-field basis states (Slater determinants, products of
spin or qubit states). This is a result of the very high energy level density
of many-body states which can be easily mixed by a residual interaction between
particles. We consider the time dynamics of wave functions and increase of
entropy in such chaotic systems.
  As an example we present the time evolution in a closed quantum computer. A
time scale for the entropy S(t) increase is t_c =t_0/(n log_2{n}), where t_0 is
the qubit ``lifetime'', n is the number of qubits, S(0)=0 and S(t_c)=1. At t <<
t_c the entropy is small: S= n t^2 J^2 log_2(1/t^2 J^2), where J is the
inter-qubit interaction strength. At t > t_c the number of ``wrong'' states
increases exponentially as 2^{S(t)} . Therefore, t_c may be interpreted as a
maximal time for operation of a quantum computer, since at t > t_c one has to
struggle against the second law of thermodynamics. At t >>t_c the system
entropy approaches that for chaotic eigenstates.
