Asymptotic thermodynamic criteria for the persistency of metastable states

The mean first exit time is logarithmically equivalent to the exponential of the smallest total free energy barrier separating metastable from stable states for a general class of discontinuous Markov processes in the thermodynamic limit. This asymptotic principle of minimum relative free energy difference constitutes a generalization of the corresponding entropy principle to systems in thermal contact with their environment and formalizes the results of a number of previous authors. The overwhelmingly most probable path of exit, in the thermodynamic limit, is the mirror image in time of the causal path. Along the anticausal path the free energy is an increasing function of time and hence does not provide any criterion of evolution. The kinetic mean-field model of a ferromagnetic serves as an illustration