Logarithmic susceptibility and optimal control of large fluctuations

We analyze the probabilities of large infrequent fluctuations in systems driven by external fields. In a broad range of the field magnitudes, the logarithm of the fluctuation probability is linear in the field magnitude, and the response can be characterized by a logarithmic susceptibility. This susceptibility is used to analyze optimal control of large fluctuations. For nonadiabatic driving, the activation energies for nucleation and for escape of a Brownian particle display singular behavior as a function of the field shape.