Maximal-entropy-production-rate nonlinear quantum dynamics compatible
with second law, reciprocity, fluctuation-dissipation, and time-energy
uncertainty relations
In view of the recent quest for well-behaved nonlinear extensions of the
traditional Schroedinger-von Neumann unitary dynamics that could provide
fundamental explanations of recent experimental evidence of loss of quantum
coherence at the microscopic level, in this paper, together with a review of
the general features of the nonlinear quantum (thermo)dynamics I proposed in a
series of papers [see references in G.P. Beretta, Found.Phys. 17, 365 (1987)],
I show its exact equivalence with the maximal-entropy-production
variational-principle formulation recently derived in S.
Gheorghiu-Svirschevski, Phys.Rev. A 63, 022105 (2001). In addition, based on
the formalism of general interest I developed for the analysis of composite
systems, I show how the variational derivation can be extended to the case of a
composite system to obtain the general form of my equation of motion, that
turns out to be consistent with the demanding requirements of strong
separability. Moreover, I propose a new intriguing fundamental ansatz: that the
time evolution along the direction of steepest entropy ascent unfolds at the
fastest rate compatible with the time-energy Heisenberg uncertainty relation.
This ansatz provides a possible well-behaved general closure of the nonlinear
dynamics, compatible with the nontrivial requirements of strong separability,
and with no need of new physical constants. In any case, the time-energy
uncertainty relation provides lower bounds to the internal-relaxation-time
functionals and, therefore, upper bounds to the rate of entropy production.Comment: RevTeX; 19 pages; submitted to Phys.Rev.A on Feb.9, 2001; revised
version submitted on Sept.14, 2001 with slightly modified derivation in
Section III, improved discussion on strong separability in Sections X and IX,
added Eqs. 64b, 64c and 11
