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Free energies and other thermodynamical quantities are investigated incanonical and grand canonical ensembles of statistical mechanics involvingunstable states which are described by the generalized eigenstates with complexenergy eigenvalues in the conjugate space of Gel'fand triplet. The theory isapplied to the systems containing parabolic potential barriers (PPB's). Theentropy and energy productions from PPB systems are studied. An equilibrium fora chemical process described by reactions $A+CB\rightleftarrows AC+B$ is alsodiscussed.Comment: 14 pages, AmS-LaTeX, no figur

Statistical mechanics for unstable states in Gel’fand triplets and investigations of parabolic potential barriers