A LINDBLADIAN OPERATOR FOR OPEN SYSTEM THERMALIZATION, WITH APPLICATIONS

Abstract

A general phenomenological expression is provided, within the frame of the Gorini-Kossakowski-Sudarshan-Lindblad formalism, for the time (t) development of the density operator ρ(t) during thermalization, namely the process such that an open system with arbitrary initial states, when coupled to a thermal bath, ρ (t -> ∞) takes up a Gibbsian form. The theory is applied to a molecular vibrating system, to a semi-classical vibronic entity, and may be applied to the excitation probabilities in a condensed state’s phonon system and to arbitrarily large-scale systems (reaching as far as global warming). A sideline is to an entropy-decreasing Maxwell-demon type quantum state transition. While the prescription may not be unique, it gives rise to an experimentally testable non-monotonicity in the system’s information entropy. The calculated entropy maximum found for an electronic doublet is interpreted as a “transient democratization” of the states and, though lacking a formal proof, a conjecture is proposed for the occurrence of maxima in general instances.