Thermally induced escape: The principle of minimum available noise energy

The average time required for thermally induced escape from a basin of attraction increases exponentially with inverse temperature in proportion to exp($E_A$/kT) in the limit of low temperature. A minimum principle states that the activation energy $E_A$ is the minimum available noise energy required to execute a state-space trajectory which takes the system from the attractor of the noise-free system to the boundary of its basin of attraction and that the minimizing trajectory is the most probable low-temperature escape path. This principle is applied to the problem of thermally induced escape from two attractors of the dc-biased Josephson junction, the zero-voltage state and the voltage state, to determine activation energies and most probable escape paths. These two escape problems exemplify the classical case of escape from a potential well and the more general case of escape from an attractor of a nonequilibrium system. Monte Carlo simulations are used to verify the accuracy of the activation energies and most probable escape paths derived from the minimum principle.