Stochastic-time description of transitions in unstable and multistable systems

The decay of a macroscopic unstable state implies anomalous fluctuations in the amplitudes of the decaying parameters, which are the transient extension of the stationary divergences at the critical point of phase transitions. These decays are best studied, theoretically and experimentally, via the stochastic times of intersection of a given threshold. Besides yielding a closed solvable set of moment equations, the stochastic time approach permits to discriminate the transient fluctuations due to the spread in the initial conditions from those arising from noise along the path. These latter ones limit the validity of the so-called asymptotic approximation. Here we develop a detailed theory including scaling laws and then compare it with experimental measurements in order to show the limit of previous approaches. © 1982 Società Italiana di Fisica.