Nonlinear quantum evolution with maximal entropy production
Abstract
We derive a well-behaved nonlinear extension of the non-relativistic Liouville-von Neumann dynamics driven by maximal entropy production with conservation of energy and probability. The pure state limit reduces to the usual Schroedinger evolution, while mixtures evolve towards maximum entropy equilibrium states with canonical-like probability distributions on energy eigenstates. The linear, near-equilibrium limit is found to amount to an essentially exponential relaxation to thermal equilibrium; a few elementary examples are given. In addition, the modified dynamics is invariant under the time-independent symmetry group of the hamiltonian, and also invariant under the special Galilei group provided the conservation of total momentum is accounted for as well. Similar extensions can be generated for, e.g., nonextensive systems better described by a Tsallis q-entropy.
Cite
@article{arxiv.quant-ph/0007111,
title = {Nonlinear quantum evolution with maximal entropy production},
author = {S. Gheorghiu-Svirschevski},
journal= {arXiv preprint arXiv:quant-ph/0007111},
year = {2009}
}
Comments
RevTex-Latex2e, 21 pg., no figures; to be published in Phys.Rev.A. Corrected minor typos, updated version of variational principle (no results change), added more comments (e.g. clarified relation to Prigogine's minimum entropy production principle, detailed possible resolution of the separability problem, etc.) and added new section outlining generalization for non-standard forms of the energy and/or entropy functionals