Distributions of First-passage and ...

The prototype problem of a pendulum connected to a heat bath with strong dissipation is common for many physical applications. The corresponding equations of motion describe the current through the Josephson junction, and phase drift in a synchronizing auto-generator, is related to the problems of "stochastic ratchets", to the motion of Brownian particles in a nonlinear system with anisotropic spatially periodic potential. The thermodynamic flux in such systems is related to the (random) particle escape time. In the present work the first-passage time distribution and its thermodynamic interpretation has been used to describe these phenomena. In particular, according to the example of auto-generator oscillating system, it is shown that the unperturbed average first-passage time is related to the value of the thermodynamic kinetic coefficient.