9.6 Non-unitary time evolution

An interesting issue discussed in the literature is the time evolution of the entanglement entropy. It was suggested in [26] that the eigenvalues of a reduced density matrix depend on time t. This is not possible if the time evolution of the density matrix is described by a unitary operator. Thus, the time evolution should be nonunitary. In particular, the entanglement entropy should depend on time t. Similar conclusions have been made in [30] and [158, 159, 160], where, in particular, it was shown that the entanglement entropy is an increasing function of time. These observations may have interesting applications for black holes. As was proposed by Hawking [129] the evolution in time of a black hole should be nonunitary, so that a pure initial state may evolve into a mixed state. From the entanglement point of view, this behavior appears not to be in contradiction with the principles of quantum mechanics, rather it is a simple consequence of the entangled nature of the system. The irreversible loss of information due to entanglement is also seen from the evolution of the entropy under the Renorm-Group (RG) flow [203, 164].
  Go to previous page Go up Go to next page