Two definitions of stability of equilibria

Abstract

In classical physics the stability of an equilibrium requires that any, even infinitesimal, displacement from the configuration of equilibrium results in forces which tend to restore the original equilibrium configuration. In case of several stable equilibrium configurations, the height of the threshold, which must be exceeded by the deviarion from the stable equilibrium in order to bring the configuration into another stable equilibrium is taken as a measure of stability of the first configuration. In quantum mechanics, and in the recent work of I. Bâianu, S. Comorosan and M. Marinescu (Bull. Math. Biophysics,30, 625–635, 1968;31, 59–70, 1969;32, 539–561, 1970) on organismic supercategories, preference is given to take, as ameasure of the degree of stability of a configuration, or of a “state”, the length of time during which the system remains in that configuration. It is shown that under rather general conditions the two criteria are equivalent.