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Towards a unified formulation of dynamics and thermodynamics. I. From microscopic to macroscopic time scales
Author(s) -
Durand Philippe,
Paidarová Ivana
Publication year - 2011
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.22584
Subject(s) - quantum , physics , statistical physics , perturbation theory (quantum mechanics) , path integral formulation , simple (philosophy) , von neumann architecture , classical mechanics , quantum mechanics , mathematics , philosophy , epistemology , pure mathematics
We go a step further on the path opened in the mid‐1950s by Prigogine and his collaborators towards a unified description of dynamics and thermodynamics of irreversible processes. Here, the theory is developed from concepts and methods originating in the quantum theory of resonances. The Liouville–von Neumann equation is solved by means of effective Liouvillians, which are similar to the effective Hamiltonians used in quantum mechanics. Hierarchies of effective Liouvillians allow us to determine the long macroscopic time scales from short microscopic characteristic times. For that purpose, standard perturbation theory is used in the complex plane. Damped and oscillating irreversible decays of a fluctuation are described by means of a two‐dimensional matrix representation of the Liouvillian. Finally, we derive a kinetic equation for a simple model of a chemical reaction proceeding towards equilibrium. The model implies a transition state assimilated to a short‐lived resonance. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011