Influence of Entropy Changes on First Passage Time in the Thermodynamics of trajectories

An ensemble of trajectories with dynamical activity and first-passage time (FPT) is considered in the context of the thermodynamics of trajectories. The relationship between the average FPT and the total change in entropy is determined, with a focus on non-negative values of the total change in entropy only. Similar dependencies were found for dynamic activity, the dispersion of dynamic activity, and FPT, as well as for the correlation between dynamic activity and FPT. Applying the obtained results to model systems reveals dependencies on entropy changes in stationary nonequilibrium and equilibrium states. To relate changes in entropy to the conjugate parameter of the FPT, three models of the distribution function are applied to classical two- and three-level systems, and to a quantum two-level system.