  We propose a generalization of the quantum entropy introduced by Wigner and
von Neumann in 1929 [Zeitschrift f\"ur Physik 57, 30 (1929)]. Our
generalization is applicable to both quantum pure states and mixed states. When
the dimension $N$ of the Hilbert space is large, as a result of typicality,
this generalized Wigner-von Neumann (GWvN) entropy becomes independent of
choices of basis and is asymptotically equal to $\ln N$. The dynamic evolution
of our entropy is also typical, reminiscent of quantum H theorem proved by von
Neumann. For the microcanonical ensemble, the GWvN entropy is equivalent to the
Boltzmann entropy; for a subsystem in a mixed state, the GWvN entropy is
equivalent to the familiar von Neumann entropy, which is zero for pure states.
The GWvN entropy can be used to derive the Gibbs ensemble.
