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.

first law of thermodynamics, heat flow, non-equilibrium, information entropy, energy spectrum, climate change.

Received: November 3, 2022; Accepted: December 5, 2022; Published: January 23, 2023

How to cite this article: R. Englman, A Lindbladian operator for open system thermalization, with applications, JP Journal of Heat and Mass Transfer 31 (2023), 99-121. http://dx.doi.org/10.17654/0973576323008

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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