EQUATIONS OF MOTION IN NONEQUILIBRIUM STATISTICAL-MECHANICS FOR NONEXTENSIVE SYSTEMS

Recent investigations of nanoscale quantum device systems and small cl usters of atoms and molecules have shown new features of both nonequil ibrium dynamics and nonextensivity. The challenge is to understand the oretically the fast dynamical processes on time scales of femtoseconds in these systems. An overview of the approaches to time-dependent non equilibrium statistical mechanics, including a critical review of the entropic methods due to Jaynes, Robertson, and Zubarev for the extensi ve nonequilibrium systems, reveals difficulties in setting up the asso ciated dynamics. We therefore propose the use of the Lindblad equation for the density matrix in place of the usual unitary Liouville-von Ne umann equation of motion because it meets all the required criteria (p ositive, trace-class, and includes the possibility of mixed to pure st ate evolution) for describing dissipative dynamics and the T sallis pr escription for handling the nonextensivity. We will explore briefly (i ) the notion of decoherence, (ii) near equilibrium linear response, (i ii) evolution of entropy, and (iv) action principle, based on these co nsiderations. Pie also exhibit a time-dependent ''mixed state'' marker for describing the nonequilibrium state of a dissipative quantum osci llator, which is a prototype of an electronic device. This investigati on, it is hoped, gives glimpses of insight into understanding the shor t time-scale dynamics of systems between the times determined by the u ncertainty principle and the decoherence clue to the heat bath. (C) 19 98 Elsevier Science B.V. All rights reserved.