Universal response functions in driven dissipative tunneling dynamics

Universality in nonlinear nonequilibrium systems is typically expressed through scaling laws that render macroscopic behavior insensitive to microscopic details. Whether such universality survives when periodic forcing and nonlocal dissipative memory act simultaneously remains an open question in driven open dynamics. Here, we demonstrate that barrier-crossing processes in periodically driven dissipative systems are governed not merely by modified exponential scaling but by an explicit two-parameter universal response function. Within a semiclassical instanton framework incorporating Floquet modulation and Ohmic environmental coupling, the tunneling exponent factorizes into a system-dependent static contribution and a universal function of two dimensionless control parameters: the normalized driving frequency and the dissipation strength. This factorization arises from the combined modification of a single saddle-point trajectory and does not introduce additional independent scaling variables. Weak-to-moderate dissipation acts as a smooth dynamical renormalization of the effective action, preserving saddle-point structure and enabling controlled analytical expansion. In the high-frequency regime, the response exhibits universal dynamical averaging, while an explicit integral representation establishes a continuous adiabatic-Floquet crossover. Direct numerical evaluation of the nonlocal instanton action confirms that the normalized tunneling exponent exhibits a universal dependence on the driving parameter that is robust across different model systems, demonstrating that driven dissipative barrier crossing defines a distinct two-parameter universality class within nonlinear nonequilibrium dynamics. These results elevate tunneling universality from scaling behavior to a predictive functional description and provide a unifying framework for response phenomena in driven systems with memory.