Abstract
We propose a generalization of the quantum entropy introduced by Wigner and von Neumann [Zeitschrift fu ̈r 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, this generalized Wigner-von Neumann (GWvN) entropy becomes independent of choices of basis and is asymptotically equal to ln N in the sense of typicality. The dynamic evolution of our entropy is also typical, reminiscent of quantum H theorem proved by von Neumann. For a composite system, the GWvN entropy is typically additive; for the microcanonical ensemble, it is equivalent to the Boltzmann entropy; for a system entangled with environment, it is consistent with the familiar von Neumann entropy, which is zero for pure states. In addition, the GWvN entropy can be used to derive the Gibbs ensemble.
Reference: Hu, Wang and Wu, arXiv: 1812.10020
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