Dynamical Lee-Yang zeros for continuous-time and discrete-time stochastic processes

We describe classical stochastic processes by using dynamical Lee-Yang zeros. The system is in contact with external leads and the time evolution is described by the two-state classical master equation. The cumulant generating function is written in a factorized form and the current distribution is characterized by the dynamical Lee-Yang zeros. We show that a continuous distribution of zeros is obtained by discretizing the time variable. When the transition probability is a periodically oscillating function of time, the distribution of zeros splits into many parts. We study the geometric property of the current by comparing the result with that of the adiabatic approximation. We also use the Floquet-Magnus expansion in the continuous-time case to study dynamical effects on the current at the fast-driving regime.