Statistical Mechanics for Unstable States in Gel'fand Triplets and Investigations of Parabolic Potential Barriers

Abstract

Free energies and other thermodynamical quantities are investigated in canonical and grand canonical ensembles of statistical mechanics involving unstable states which are described by the generalized eigenstates with complex energy eigenvalues in the conjugate space of Gel'fand triplet. The theory is applied to the systems containing parabolic potential barriers (PPB's). The entropy and energy productions from PPB systems are studied. An equilibrium for a chemical process described by reactions $A+CB\rightleftarrows AC+B$ is also discussed.

14 pages, AmS-LaTeX, no figure

References in corpus (4)

• Operator Methods of the Parabolic Potential Barrier
• Stationary Flows of the Parabolic Potential Barrier in Two Dimensions
• Entropy Burst from Parabolic Potentials
• Statistical Mechanics for States with Complex Eigenvalues and Quasi-stable Semiclassical Systems

Cited by in corpus (6)

• Theoretical Analysis of Dynamic Processes for Interacting Molecular Motors
• Correlations and Symmetry of Interactions Influence Collective Dynamics of Molecular Motors
• Zero Energy Solutions and Vortices in Schroedinger Equations
• The Definition of Entropy for Quantum Unstable Systems: A View-Point Based on the Properties of Gamow States
• Exclusion process on an open lattice with fluctuating boundaries
• Zero-Energy Flows and Vortex Patterns in Quantum Mechanics